1
In Activity 1, (5, 3) means —
💡 Hint:
The column is written first.
Explanation:
Column 5 and row 3. (3, 5) is another desk.
Class 9 · Maths · Chapter 3 · बिहार बोर्ड (BSEB)CBSE · NCERT 2026-27
Coordinate Geometry
Coordinate Geometry
How to use this page:
1. Read — Activity 1 seating · Exercise 3.1 · Cartesian plane · Exercise 3.2 · plotting · Activity 2 dice · Exercise 3.3, diagram, worked example, board tip
2. Check — each lesson has its own questions; the number follows the lesson
3. Mastery ★ — all of that lesson correct. Redo the wrong ones
4. The memory figure shows the signs of the four quadrants — first (+, +), second (−, +), third (−, −) and fourth (+, −).
In the 15-chapter Bihar book this is chapter 3. Ganita Manjari 2026-27 uses a different order. Progress stays in this browser.
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- 1 Two facts and a seating plan — Activity 1
- 2 The Cartesian plane and the four quadrants
- 3 Abscissa, ordinate, and points on the axes
- 4 Plotting a point when the coordinates are given
- 5 The dice game — Activity 2
- 6 The distance between two plotted points
- Chapter winner — every lesson at mastery ★
🎬 Shorts
This chapter has no Short on the channel yet, so ten empty cards are not shown. The notes, diagrams and checks are complete.
📄 PDF download — notes + answer key
Two facts and a seating plan — Activity 1
दो सूचनाएँ और बैठक योजना — क्रियाकलाप 1 · Textbook 3.1 · Activity 1 · Exercise 3.1
One reference is not enoughNotes
A street number without a house number does not find the house. A dot on paper is not fixed by saying “it is near the top”. A place in a plane needs two independent facts — two distances from two fixed lines.
Descartes brought the idea of latitude and longitude onto a plane. That is why the method is called Cartesian. The chapter starts here, not with a formula.
Activity 1 — the seating planActivity
Push the desks together and draw the classroom. Let each desk be a square and write the name of the student in it. The place is two facts: which column, and which row.
Write the fifth column and the third row as (5, 3). Column first, then row. (3, 5) is not that seat. If Sonia sits in the fourth column and the first row, write S(4, 1). The teacher desk is not part of the plan. The teacher is only an observer.
Worked exampleExample
Question: In Exercise 3.1, how many crossings can be called (4, 3)? The scale is 1 cm = 200 m.
Answer: The street in one direction and the street in the other meet at one crossing. (4, 3) is exactly one crossing. (3, 4) is a different crossing. The order is part of the name, so do not count them as one.
10-second revision
- A plane needs two facts
- Activity 1: column first, then row
- (5, 3) and (3, 5) are different desks
Board tip · BSEBBoard tip
In Exercise 3.1 both (4, 3) and (3, 4) have the answer 1. When a map is drawn, keep the scale 1 cm = 200 m.
Board tip · CBSEBoard tip
The Cartesian name comes from Descartes. If the paper asks for the name of the system, write Cartesian, not only “graph”.
Check your understandingall correct = mastery ★
2
In the seating plan, (5, 3) and (3, 5) are the same seat.
Explanation:
False — a change of order changes the column and the row.
3
In Activity 1 the teacher is treated as an ______ of the plan.
💡 Hint:
The teacher desk is not on the plan.
Explanation:
An observer. The desks belong to the students.
4
How many distances are needed at least to fix a dot on paper?
💡 Hint:
The left edge and the bottom line.
Explanation:
Two distances. Distance from one edge does not fix the place.
5
How would you describe the position of a lamp on your table to another person? Write two measurements.
Model answer (board format)
Give the perpendicular distance from the left edge of the table and the perpendicular distance from the front edge. One distance alone does not fix the lamp.
Check your answer:
The Cartesian plane and the four quadrants
कार्तीय तल और चार चतुर्थांश · Textbook 3.2 · axes · signs
Two number lines crossNotes
On a number line, positive counts go to the right of the origin and negative counts to the left. Take two such lines. The horizontal line X′X is the x-axis and the vertical line Y′Y is the y-axis. They cross at their zeros. The crossing is the origin O. OX and OY are the positive directions. OX′ and OY′ are the negative directions.
The axes divide the plane into four parts. These are the quadrants, counted I, II, III, IV anticlockwise from OX. The whole plane is the axes together with these four parts. It is called the Cartesian plane, the coordinate plane, or the xy-plane.
| Quadrant | Signs | Enclosed by |
|---|---|---|
| First | (+, +) | Positive x and positive y |
| Second | (−, +) | Negative x and positive y |
| Third | (−, −) | Negative x and negative y |
| Fourth | (+, −) | Positive x and negative y |
Worked exampleExample
Question: In which quadrant is the point (−3, 4)?
Answer: x = −3 is negative and y = 4 is positive. The signs (−, +) belong to the second quadrant. The point is to the left of the y-axis and above the x-axis.
10-second revision
- x-axis horizontal, y-axis vertical
- The origin is the zero of both axes
- Quadrants anticlockwise: (+,+), (−,+), (−,−), (+,−)
Board tip · BSEBBoard tip
The signs of the second and the fourth quadrant are often swapped. Negative x and positive y is the second. Positive x and negative y is the fourth.
Board tip · CBSEBoard tip
Do not write the count as clockwise. The book counts I, II, III, IV anticlockwise from OX.
Check your understandingall correct = mastery ★
1
The sign pattern of the second quadrant is —
💡 Hint:
Upper left.
Explanation:
(−, +). x is negative and y is positive.
2
The coordinates of the origin are (0, 0).
Explanation:
True — the distance from both axes is zero.
3
The horizontal line X′X is called the ______.
💡 Hint:
The vertical line is the y-axis.
Explanation:
The x-axis. Y′Y is the y-axis.
4
The point (−2, −5) lies in —
💡 Hint:
Both coordinates are negative.
Explanation:
The third quadrant, signs (−, −).
5
The quadrants are counted clockwise from OX.
Explanation:
False — the count is anticlockwise: I, II, III, IV.
6
Write the signs of the four quadrants in order and say which way they are counted.
Model answer (board format)
First (+, +), second (−, +), third (−, −), fourth (+, −). The count is anticlockwise from the positive x-axis.
Check your answer:
Abscissa, ordinate, and points on the axes
भुज, कोटि और अक्ष पर बिंदु · Textbook 3.2 · abscissa · ordinate
The distance is written with a signNotes
The perpendicular distance of a point from the y-axis, measured along the x-axis, is its x-coordinate. It is also called the abscissa. The perpendicular distance from the x-axis, measured along the y-axis, is the y-coordinate, or the ordinate. The positive direction gives a positive sign and the negative direction a negative sign. Write the abscissa first, then the ordinate, in brackets.
Every point on the x-axis has ordinate 0, so the form is (x, 0). Every point on the y-axis has abscissa 0, so the form is (0, y). The origin is (0, 0). These points do not lie in a quadrant.
Worked exampleExample
Question: Point A is on the x-axis, 4 units from the origin in the positive direction. B is on the y-axis, 3 units from the origin in the positive direction. Write the coordinates.
Answer: The distance of A from the y-axis is 4 units and from the x-axis is 0, so A is (4, 0). The distance of B from the x-axis is 3 units and from the y-axis is 0, so B is (0, 3). The unit is the one chosen on the axes.
10-second revision
- Abscissa = x-coordinate, ordinate = y-coordinate
- x-axis: (x, 0) · y-axis: (0, y)
- A point on an axis is not in a quadrant
Board tip · BSEBBoard tip
Do not swap the names abscissa and ordinate. The abscissa comes first. The ordinate is second.
Board tip · CBSEBoard tip
Do not put (−1, 0) in the third quadrant. It lies on the negative x-axis.
Check your understandingall correct = mastery ★
1
A point on the x-axis has the form —
💡 Hint:
The ordinate is zero.
Explanation:
(x, 0). On the y-axis it is (0, y).
2
The point (0, 4) lies on the y-axis.
Explanation:
True — the abscissa is 0, so the point is on the vertical axis.
3
The coordinates of the origin are ______.
💡 Hint:
Both distances are zero.
Explanation:
(0, 0).
4
Of the points (−1, 0), (0, 5) and (2, −3), which lie on an axis and which lie in a quadrant? Name them.
Model answer (board format)
(−1, 0) is on the negative x-axis. (0, 5) is on the positive y-axis. (2, −3) is in the fourth quadrant because the signs are (+, −). Points on an axis are not counted in a quadrant.
Check your answer:
Plotting a point when the coordinates are given
निर्देशांक देकर बिंदु आलेखित करना · Textbook 3.3 · ordered pair · Exercise 3.3
The point is placed by walking from the originNotes
Plotting means placing a point at the given coordinates. For (3, 5), walk 3 units from the origin along the positive x-axis, then 5 units from there in the positive y direction. The point lies in the first quadrant. For (5, −4), take 5 on x and then 4 in the negative y direction. That is the fourth quadrant.
State the scale on both axes, for example 1 cm = 1 unit. (x, y) is an ordered pair. If x ≠ y, then (x, y) and (y, x) are different places. If x = y, they are the same point.
Worked exampleExample
Question: Where are the Exercise 3.3 points (−2, 4), (3, −1), (−1, 0), (1, 2) and (−3, −5)?
Answer: (−2, 4) is in the second quadrant. (3, −1) is in the fourth. (−1, 0) is on the negative x-axis, not in a quadrant. (1, 2) is in the first. (−3, −5) is in the third. Check by plotting them on the same scale.
10-second revision
- Walk x first, then y
- Ordered pair: a new order is a new place
- (−1, 0) is on an axis, not in a quadrant
Board tip · BSEBBoard tip
Exercise 3.3 uses (−1, 0) as a trap. Write the axis, not a quadrant.
Board tip · CBSEBoard tip
On a plot keep the same scale on both axes unless the question asks for another scale. Write the unit.
Check your understandingall correct = mastery ★
1
The correct order for plotting (3, 5) is —
💡 Hint:
The abscissa comes first.
Explanation:
From the origin, 3 units on positive x, then 5 units on positive y.
2
If x ≠ y, then (x, y) and (y, x) are the same point.
Explanation:
False — order matters. They are equal only when x = y.
3
(x, y) is called an ordered ______.
💡 Hint:
The order must not be swapped when x ≠ y.
Explanation:
An ordered pair.
4
Which statement about (5, 2) and (2, 5) is correct?
💡 Hint:
5 ≠ 2.
Explanation:
They are different points because the coordinates are not equal.
5
Write the steps to plot (−2, 4). Also name the quadrant. Scale: 1 cm = 1 unit.
Model answer (board format)
Take 1 cm = 1 unit on both axes. From the origin walk 2 units along the negative x-axis. From there walk 4 units in the positive y direction and mark the point. The signs are (−, +), so the point is in the second quadrant.
Check your answer:
The dice game — Activity 2
पासे वाला खेल — क्रियाकलाप 2 · Textbook 3.3 · Activity 2
Activity 2 — the race to (10, 10)Activity
Two players, two counters or coins, graph paper, and two dice of different colours — red and green. Both counters start at (0, 0). The red die increases x and the green die increases y.
A red 3 and a green 1 move the counter to (3, 1). Next, a red 1 and a green 4 move it to (3 + 1, 1 + 4) = (4, 5). The player who reaches (10, 10) first, without going past it, wins. If the abscissa or the ordinate would exceed 10, the turn is missed. Counters may not share a point. If you land on the other player, that counter returns to (0, 0).
The addition keeps the same orderNotes
Each move adds a new pair to the old pair. The red die is added to x and the green die to y. The axes are still called x and y. On a time-distance graph the names of the axes may change, but the rule of an ordered pair does not.
Worked exampleExample
Question: The counter is at (6, 8). The red die shows 3 and the green die shows 4. Is the move allowed?
Answer: The new place would be (6 + 3, 8 + 4) = (9, 12). The ordinate 12 is greater than 10, so the counter would pass the target. The turn is missed and the counter stays at (6, 8).
10-second revision
- Start (0, 0), target (10, 10)
- Red die is x, green die is y
- A move past 10 is lost; a clash sends the other counter to the origin
Board tip · BSEBBoard tip
Activity 2 comes after Activity 1. In an answer write both the colour of the die and the axis.
Board tip · CBSEBoard tip
Reaching the target and passing the target are different. Passing it is not a win.
Check your understandingall correct = mastery ★
1
From (0, 0), a red 3 and a green 1 move the counter to —
💡 Hint:
Red is x.
Explanation:
(3, 1). Green is added to y.
2
A move is still allowed if the abscissa becomes 11, because the counter got close to the target.
Explanation:
False — if the abscissa or the ordinate would exceed 10, the turn is missed.
3
If your counter lands on the other player, that counter returns to ______.
💡 Hint:
The starting place.
Explanation:
(0, 0).
4
The counter is at (2, 4). The next throw is red 5 and green 1. Find the new place and say whether the move is allowed.
Model answer (board format)
The new place is (2 + 5, 4 + 1) = (7, 5). Both coordinates are less than 10, so the move is allowed. The counter moves to (7, 5).
Check your answer:
The distance between two plotted points
दो अंकित बिंदुओं के बीच की दूरी · The measure after plotting · Pythagoras
Once the coordinates are known, the straight distance followsNotes
The exercises of this chapter ask you to name a point and to plot it. The straight distance between two such points is a further measurement. Join (x₁, y₁) and (x₂, y₂). The horizontal gap is x₂ − x₁ and the vertical gap is y₂ − y₁. These are the sides of a right triangle.
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]. The square removes a negative sign. The square root gives a length, so the distance is not negative. Keep the unit that was chosen on the axes.
Worked exampleExample
Question: Find the distance between A(1, 2) and B(4, 6). On the axes, 1 unit = 1 cm.
Formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²]
Substitution: d = √[(4 − 1)² + (6 − 2)²] = √(3² + 4²) = √(9 + 16) = √25 = 5
Unit: 5 cm.
10-second revision
- Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]
- The square root comes after the squares
- Distance is not negative; the unit is the axis unit
Board tip · BSEBBoard tip
Do not write the distance as the sum of the gaps. For gaps 3 and 4, 3 + 4 = 7 is wrong. √(9 + 16) = 5 is right.
Board tip · CBSEBoard tip
Write the unit in the answer. The formula, the substitution and the unit should all appear in one answer.
Check your understandingall correct = mastery ★
1
The distance between (0, 0) and (3, 4) is —
💡 Hint:
√(9 + 16).
Explanation:
√(3² + 4²) = √25 = 5 units.
2
In the distance formula it is enough to write the sum of the squares and leave out the square root.
Explanation:
False — the sum is in square units. A length needs the square root.
3
The distance between A(1, 2) and B(4, 6) is 5 ______ when 1 unit = 1 cm.
💡 Hint:
The unit of the axes.
Explanation:
5 cm.
4
The correct distance formula is —
💡 Hint:
Pythagoras, then the root.
Explanation:
Inside the square root, the squares of both gaps are added.
5
Find the distance between P(−1, 2) and Q(2, 6). Write the formula, the substitution and the unit. 1 unit = 1 cm.
Model answer (board format)
d = √[(x₂ − x₁)² + (y₂ − y₁)²] = √[(2 − (−1))² + (6 − 2)²] = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.
Check your answer:
6
The distance between two different points can be less than zero.
Explanation:
False — a length under a square root is not negative. For different points the distance is positive.
❓ Full question bank — with answers and explanations — 65 questions
Pick a type. The 30 lesson checks are separate — each lesson has as many as its topic needs. All correct earns mastery ★.
BSEB modelpractice · not annual60 tried · 0 correctMultiple choiceMCQ130 tried · 0 correctTrue / falseTrue / false80 tried · 0 correctFill in the blanksFill80 tried · 0 correctMatchMatch20 tried · 0 correctAssertion–reasonAssertion–reason50 tried · 0 correctBalancingBalancing40 tried · 0 correctIdentifyIdentify20 tried · 0 correctShort and longVSA, SA, LA110 tried · 0 correctCBSE-stylenot a PYQ60 tried · 0 correct
No question is marked as a verified past paper. The BSEB set is a model for practice. CBSE items are CBSE-style, not a copy of any year’s paper.
Multiple choice
0/13Pick one option. A wrong try brings a hint.
1
Independent facts needed to fix a point in a plane are —
💡 Hint:
On a line, one number is enough.
Explanation:
Two. One horizontal reference and one vertical.
2
The horizontal axis is called —
💡 Hint:
Y′Y is vertical.
Explanation:
X′X is the x-axis.
3
The signs in the fourth quadrant are —
💡 Hint:
Positive x, negative y.
Explanation:
(+, −).
4
The origin is —
💡 Hint:
Both distances are zero.
Explanation:
(0, 0).
5
A point on the y-axis has the form —
💡 Hint:
The abscissa is zero.
Explanation:
(0, y).
6
The point (−6, −2) lies in —
💡 Hint:
Both negative.
Explanation:
The third quadrant.
7
The point (3, −4) lies in —
💡 Hint:
Positive x, negative y.
Explanation:
The fourth quadrant.
8
(4, 3) and (3, 4) are —
💡 Hint:
4 ≠ 3.
Explanation:
The order differs, so the points differ.
9
The abscissa is —
💡 Hint:
The ordinate is y.
Explanation:
The abscissa is the x-coordinate.
10
The distance between (0, 0) and (6, 8) is —
💡 Hint:
√(36 + 64).
Explanation:
√(36 + 64) = √100 = 10 units.
11
In Activity 1 the first number written is —
💡 Hint:
In (5, 3) the 5 is the column.
Explanation:
The column. The row is the second number.
12
Red 2 and green 4, from (0, 0), move the counter to —
💡 Hint:
Red is x.
Explanation:
(2, 4).
13
The point (−5, 0) lies —
💡 Hint:
The ordinate is 0.
Explanation:
On the negative x-axis. That is not a quadrant.
True or false
0/81
In the Cartesian plane the x-axis is vertical.
Explanation:
False — the x-axis is horizontal. The y-axis is vertical.
2
In the first quadrant both coordinates are positive.
Explanation:
True — the signs are (+, +).
3
The point (0, −4) lies on the x-axis.
Explanation:
False — the abscissa is 0, so it lies on the negative y-axis.
4
If x = y, then (x, y) and (y, x) are the same point.
Explanation:
True — when the two numbers are equal, a change of order does not move the point.
5
In Activity 2 the green die increases the x-coordinate.
Explanation:
False — the green die increases y. The red die increases x.
6
The distance formula adds the squares of both gaps and then takes the square root.
Explanation:
True — that is the Pythagoras form.
7
Every point on an axis lies in some quadrant.
Explanation:
False — the quadrants are the regions between the axes. The axes themselves are not counted in them.
8
In Exercise 3.1, (4, 3) and (3, 4) are the same crossing.
Explanation:
False — a change of order is a crossing of different streets. Each name is exactly one crossing.
Fill in the blanks
0/81
The point where the axes cross is called the ______.
💡 Hint:
The origin.
Explanation:
The coordinates are (0, 0).
2
The y-coordinate is also called the ______.
💡 Hint:
The ordinate.
Explanation:
The abscissa is x.
3
The quadrants are counted in the ______ direction.
💡 Hint:
Anticlockwise.
Explanation:
Starting at OX.
4
The ordinate of a point on the x-axis is ______.
💡 Hint:
0.
Explanation:
The form is (x, 0).
5
In the distance formula the ______ of both gaps are added.
💡 Hint:
The squares.
Explanation:
Then the square root.
6
The target point of Activity 2 is ______.
💡 Hint:
(10, 10).
Explanation:
The start is (0, 0).
7
A point with positive x and negative y is in the ______ quadrant.
💡 Hint:
The fourth.
Explanation:
The signs are (+, −).
8
At 1 cm = 1 unit, the distance from (0, 0) to (8, 6) is ______ cm.
💡 Hint:
10.
Explanation:
√(64 + 36) = √100.
Match
0/21
Match the word with its meaning.
Column B: A. The y-coordinate · B. (0, 0) · C. One fourth of the plane · D. The x-coordinate
1. Abscissa
2. Ordinate
3. Origin
4. Quadrant
Explanation:
The abscissa is x, the ordinate is y, the origin is (0, 0), and a quadrant is a fourth of the plane.
2
Match the point with its place.
Column B: A. First · B. Second · C. Third · D. Fourth
1. (2, 3)
2. (−2, 3)
3. (−2, −3)
4. (2, −3)
Explanation:
The signs in order are (+,+), (−,+), (−,−), (+,−).
Assertion–reason
0/5Check both statements, then see whether the reason explains the assertion.
1
Assertion (A): (5, 1) and (1, 5) are different points.
Reason (R): (x, y) is an ordered pair and here the two numbers are not equal.
Explanation:
Both are true and R is the correct reason.
2
Assertion (A): The coordinates of the origin are (0, 0).
Reason (R): The signs of the first quadrant are (+, +).
Explanation:
Both are true, but R does not explain the origin.
3
Assertion (A): A point on the x-axis has the form (x, 0).
Reason (R): On the x-axis the abscissa is always zero.
Explanation:
A is true. R is false — on the x-axis the ordinate is zero, not the abscissa.
4
Assertion (A): (−4, 0) lies in the second quadrant.
Reason (R): When the ordinate is zero, the point lies on the x-axis.
Explanation:
A is false. R is true — this is why the point is not in a quadrant.
5
Assertion (A): The distance between (0, 0) and (5, 12) is 13 units.
Reason (R): √(5² + 12²) = √(25 + 144) = √169 = 13.
Explanation:
Both are true and R explains A by the calculation.
Coefficient practice
0/4These are not results of the maths chapter. They are only coefficient practice for H2 + O2 → H2O.
1
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). Complete the count for the water molecule.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
2
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). Keep the hydrogen atoms equal on both sides.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
3
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). Keep the oxygen atoms equal on both sides.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
4
This is coefficient practice, not a result of this maths chapter. Fill coefficients for H2 + O2 making H2O (blank = 1). A blank means the coefficient 1.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
Classify
0/21
Place each point in its region.
(1, 2)
(−1, 2)
(0, 2)
(3, 0)
Explanation:
(1, 2) is in the first, (−1, 2) in the second, and (0, 2) and (3, 0) are on the axes.
2
Place each statement in the right class.
Column first, then row
The red die increases x
The teacher is an observer
The target is (10, 10)
Explanation:
The seating plan is Activity 1. The dice and (10, 10) are Activity 2.
Very short answer
0/51
What is the Cartesian plane?
Model answer (board format)
The plane formed by two perpendicular number lines X′X and Y′Y is the Cartesian plane. Their crossing is the origin.
Check your answer:
2
Define abscissa and ordinate in one line each.
Model answer (board format)
The abscissa is the x-coordinate of the point. The ordinate is the y-coordinate of the point.
Check your answer:
3
Name the quadrants of (−3, 5) and (2, −4).
Model answer (board format)
(−3, 5) is in the second quadrant. (2, −4) is in the fourth quadrant.
Check your answer:
4
Why are the coordinates of the origin (0, 0)?
Model answer (board format)
The origin lies on both axes, so both perpendicular distances are zero.
Check your answer:
5
Write the distance between (0, 0) and (3, 4), with the unit.
Model answer (board format)
√(3² + 4²) = √25 = 5 units.
Check your answer:
Short answer
0/31
Write the signs of the four quadrants. What about a point on an axis?
Model answer (board format)
First (+, +), second (−, +), third (−, −), fourth (+, −). A point on an axis is not in a quadrant. On the x-axis it is (x, 0) and on the y-axis it is (0, y).
Check your answer:
2
Find the distance between A(−2, 1) and B(2, 4). Write the formula, the substitution and the unit. 1 unit = 1 cm.
Model answer (board format)
d = √[(2 − (−2))² + (4 − 1)²] = √(4² + 3²) = √(16 + 9) = √25 = 5 cm.
Check your answer:
3
Write three rules of Activity 2: the colour of the dice, the limit 10, and a clash.
Model answer (board format)
The red die adds to x and the green die to y. Neither coordinate may exceed 10, or the turn is missed. If you land on the other counter, it returns to (0, 0).
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Long answer
0/31
Describe the Cartesian plane and say where (2, 3), (−2, 3), (−2, −3) and (2, −3) lie. Then find the distance between (2, 3) and (2, −3). 1 unit = 1 cm.
Model answer (board format)
The x-axis is horizontal and the y-axis is vertical, crossing at (0, 0). The points lie in the first, second, third and fourth quadrants in that order. The distance is √[(2 − 2)² + (−3 − 3)²] = √(0 + 36) = 6 cm.
Check your answer:
2
State the places of the five Exercise 3.3 points (−2, 4), (3, −1), (−1, 0), (1, 2) and (−3, −5). Separately say why (x, y) is called an ordered pair.
Model answer (board format)
In order: second quadrant, fourth quadrant, negative x-axis, first quadrant, third quadrant. (x, y) is an ordered pair because if x ≠ y then (y, x) is a different place.
Check your answer:
3
Find the distance from P(1, 1) to Q(4, 5). Then, as in Activity 2, show why adding (3, 4) to (1, 1) gives Q. 1 unit = 1 cm.
Model answer (board format)
d = √[(4 − 1)² + (5 − 1)²] = √(9 + 16) = √25 = 5 cm. The sum is (1 + 3, 1 + 4) = (4, 5), which is Q. A red 3 and a green 4 would be a move of that kind.
Check your answer:
BSEB model paper · practice
0/6This model set is for practice. It is not a question from any year’s annual examination. Annual questions will be added only when a source page is available.
1
A point in the second quadrant can be —
💡 Hint:
The signs are (−, +).
Explanation:
(−4, 5).
2
The point (7, 0) lies —
💡 Hint:
The ordinate is zero.
Explanation:
On the positive x-axis.
3
Another name for the ordinate is the ______.
💡 Hint:
The y-coordinate.
Explanation:
The abscissa is x.
4
The signs of quadrant III are (−, −).
Explanation:
True.
5
Find the distance between (0, 0) and (8, 15). Write the formula and the unit.
Model answer (board format)
d = √(8² + 15²) = √(64 + 225) = √289 = 17 units.
Check your answer:
6
This is coefficient practice, not a result of coordinate geometry. Balance H2 + O2 making H2O by filling coefficients (blank = 1).
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
CBSE-style questions
0/6These are competency-based practice questions. They are not copies of a CBSE paper.
1
A student places (−3, 4) in the fourth quadrant. The mistake is —
💡 Hint:
The real signs are (−, +).
Explanation:
(−3, 4) is in the second quadrant. The student swapped the signs.
2
(5, 0) and (0, 5) are shown as one point on a graph. The conclusion is —
💡 Hint:
One is on one axis, the other on the other axis.
Explanation:
(5, 0) is on the x-axis and (0, 5) is on the y-axis. They are not one point.
3
Assertion (A): In Activity 2 a move of red 2 and green 1 from (9, 8) should be missed.
Reason (R): Passing the target is the winning rule.
Explanation:
A is true because x would become 11. R is false — passing the target cancels the move.
4
Writing the distance as √[(x₂ − x₁) + (y₂ − y₁)] is the correct formula.
Explanation:
False — the squares of the gaps are added, then the square root.
5
On a map the school is (1, 2) and the house is (4, 6). The scale is 1 cm = 1 km. Find the distance and say why (2, 1) is not the school.
Model answer (board format)
d = √[(4 − 1)² + (6 − 2)²] = √(9 + 16) = 5 km. (2, 1) is a different place because the order changed, so it is not the school.
Check your answer:
6
The counter is at (7, 9). A partner throws red 4 and green 2. What happens? Also give one example of an allowed move.
Model answer (board format)
(7 + 4, 9 + 2) = (11, 11). Both coordinates exceed 10, so the turn is missed and the counter stays at (7, 9). Red 1 and green 1 is allowed: (8, 10).
Check your answer:
🏛️ Board exam corner — Bihar Board (BSEB)— CBSE
Switch board with BSEB | CBSE above. The lessons follow the same NCERT chapter.
BSEB model · practiceBoard tip
This page has no verified annual-exam question, because no source page has been added. The model set below is practice in the board pattern.
🏛️ Model questions on one page →
The verified label will be used only when a source page for the question is available.
CBSE-style · competency-based
These are case and assertion-reason practice items. Do not treat them as past CBSE questions.
🔁 Spaced review — today’s questions
Wrong questions return soon; correct ones return after a few days.
🧠 What you learned + equation sheet
What you learned
- A point in a plane needs two perpendicular distances.
- The x-axis is horizontal, the y-axis is vertical, and they meet at the origin (0, 0).
- Quadrants are counted anticlockwise: (+, +), (−, +), (−, −), (+, −).
- The abscissa is x and the ordinate is y. On an axis one coordinate is zero.
- (x, y) is an ordered pair. If x ≠ y, then (y, x) is a different point.
- The distance between two points is √[(x₂ − x₁)² + (y₂ − y₁)²] units.
| What | Keep this |
|---|---|
| Origin | (0, 0) |
| First quadrant | (+, +) |
| Second quadrant | (−, +) |
| Third quadrant | (−, −) |
| Fourth quadrant | (+, −) |
| Distance | √[(x₂−x₁)²+(y₂−y₁)²] |
The notes are original writing. The textbook was used only for activity order and numbers. “Verified” will be used only on a question that has a source page.