Class 9 Maths Test Paper Chapter - Coordinate Geometry and Number System | CBSE Board | Detailed Solutions & Marking Scheme

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VEDANT SKILL ASSESSMENT SERIES - Academic Year 2026-27

Class: 9 | Subject: Mathematics | Chapter: 3 - Coordinate Geometry

Maximum Marks: 30 | Time Allowed: 1 Hour

GENERAL INSTRUCTIONS

  1. Read all questions carefully before answering. - Misreading the question and then blaming the paper will not increase your marks.

  2. Show proper steps wherever required. - “Sir, answer toh yahi aana tha” is not an accepted mathematical method.

  3. Write neatly and clearly. - If your handwriting requires a decoder machine, checking may become an adventure.

  4. Manage your time wisely. - Spending 45 minutes on one question and calling the rest “optional” is not a strategy.

  5. If you do not know the answer, you may cry silently. - Loud crying, emotional speeches, and negotiations for hints are strictly prohibited.

SECTION A (7 Marks)

Q1. The point of intersection of the horizontal axis and vertical axis in a Cartesian plane is called: A. Abscissa

B. Ordinate

C. Origin

D. Quadrant

Q2. The signs of coordinates of a point lying in the third quadrant (Quadrant III) are: A. (+, +)

B. (-, +)

C. (+, -)

D. (-, -)

Q3. If the coordinates of a point are given as (0, -5), then this point lies on the: A. Positive x-axis

B. Negative x-axis

C. Positive y-axis

D. Negative y-axis

Q4. The abscissa of any point on the vertical y-axis is always: A. 0

B. 1

C. -1

D. Any real number

Q5. The distance of the point P(4, 3) from the horizontal x-axis is: A. 4 units

B. 3 units

C. 7 units

D. 1 unit

Direction for Q6-Q7: For the following questions, two statements are given - one labeled Assertion (A) and the other labeled Reason (R). Select the correct answer from the options below:

A. Both A and R are true, R is correct explanation of A

B. Both A and R are true, R is not correct explanation of A

C. A is true, R is false

D. A is false, R is true

Q6. Assertion (A): The point M(-3, 4) lies completely in the second quadrant (Quadrant II). Reason (R): In the second quadrant, the x-coordinate (abscissa) is negative and the y-coordinate (ordinate) is positive. Q7. Assertion (A): The coordinate points (2, 5) and (5, 2) represent the exact same position on a Cartesian plane. Reason (R): The order of numbers in an ordered pair (x, y) is significant if x is not equal to y. ### SECTION B (8 Marks)

Q8. Write down the quadrant or axis on which each of the following given coordinate points lie:

(i) A(-4, -2)

(ii) B(3, -5)

(iii) C(0, 7)

(iv) D(-2, 0)

Q9. Find the values of the coordinates based on the following specific geometric definitions:

(i) A point whose abscissa is -3 and ordinate is 4.

(ii) A point whose ordinate is -6 and lies exactly on the vertical y-axis.

Q10. If the perpendicular distance of a point P from the x-axis is 5 units directly downwards, and its perpendicular distance from the y-axis is 3 units to the left, determine the exact ordered pair coordinates of point P.

Q11. Define the Cartesian plane. Name the horizontal line, the vertical line, and the four regions into which these intersecting lines divide the complete plane surface.

SECTION C (6 Marks)

Q12. Three vertices of a rectangle are given as O(0, 0), A(5, 0), and C(0, 3). Without plotting on a full grid sheet, find the missing coordinate of the fourth vertex B to complete the closed rectangular structure. Justify your answer using basic properties.

Q13. Plotting structural coordinates gives information about a shape. If P(-1, 2), Q(3, 2), and R(-1, -2) are three vertices of a figure, what is the length of side PQ and side PR in coordinate units?

SECTION D (5 Marks)

Q14. Answer the following questions based on the coordinate points K(-3, 2), L(4, 5), M(2, -3), and N(-5, -4):

(i) State the abscissa of point K and the ordinate of point M.

(ii) Calculate the value of: (Abscissa of L) - (Abscissa of N).

(iii) Calculate the value of: (Ordinate of K) + (Ordinate of N).

SECTION E (4 Marks)

Q15. Case Study Based Question

An urban planner overlays a Cartesian coordinate system over a park layout map to track the locations of key amenities. On this layout grid, the central administrative office is anchored perfectly at the origin O(0, 0). The main water fountain is placed at point F(3, 4), the children's play area is at P(-4, 2), and the main entry gate is situated at point G(5, -3).

Sub-questions: (i) Identify the specific quadrants in which the children's play area P and the main entry gate G are located. (1 Mark)

(ii) If a new cafeteria is to be built exactly at a position whose abscissa matches the play area P and whose ordinate matches the water fountain F, write down the coordinates of the cafeteria. (1 Mark)

(iii) Find the total perpendicular distance of the water fountain F(3, 4) from the horizontal reference line (x-axis) and vertical reference line (y-axis). Sum these two distances together. (2 Marks)

VEDANT SKILL ASSESSMENT SERIES

ACADEMIC YEAR 2026-27

Class: IX | Subject: Mathematics
Chapter: 3 - Coordinate Geometry

ANSWER KEY WITH MARKING SCHEME

SECTION A (7 MARKS)

Q1. Correct Answer: C. Origin [1]

Marking Scheme:

  • Correct option selected = 1 mark

Q2. Correct Answer: D. (-, -) [1]

In the third quadrant:

x-coordinate is negative and y-coordinate is negative.

Marking Scheme:

  • Correct option selected = 1 mark

Q3. Correct Answer: D. Negative y-axis [1]

Given point = (0, -5)

Since x = 0, the point lies on the y-axis.

Since y is negative, it lies on the negative y-axis.

Marking Scheme:

  • Correct option selected = 1 mark

Q4. Correct Answer: A. 0 [1]

The abscissa (x-coordinate) of every point on the y-axis is always 0.

Marking Scheme:

  • Correct option selected = 1 mark

Q5. Correct Answer: B. 3 units [1]

Distance from x-axis = absolute value of y-coordinate

= |3|

= 3 units

Marking Scheme:

  • Correct option selected = 1 mark

Q6. Correct Answer: A [1]

Assertion (A): True

Point M(-3, 4)

x-coordinate = negative

y-coordinate = positive

Hence, it lies in Quadrant II.

Reason (R): True

In Quadrant II:

x-coordinate is negative and y-coordinate is positive.

R correctly explains A.

Marking Scheme:

  • Correct option selected = 1 mark

Q7. Correct Answer: D [1]

Assertion (A): False

(2, 5) and (5, 2) are different points.

Reason (R): True

The order in an ordered pair (x, y) is important.

Therefore, R is true.

Marking Scheme:

  • Correct option selected = 1 mark

SECTION B (8 MARKS)

Q8. State the quadrant or axis for each point. [2]

(i) A(-4, -2) → Quadrant III

(ii) B(3, -5) → Quadrant IV

(iii) C(0, 7) → Positive y-axis

(iv) D(-2, 0) → Negative x-axis

Marking Scheme:

  • Any two correct = 1 mark

  • All four correct = 2 marks

Q9. Find the coordinates. [2]

(i) Abscissa = -3, ordinate = 4

Coordinates = (-3, 4)

(ii) Ordinate = -6 and lies on y-axis

On y-axis, x = 0

Coordinates = (0, -6)

Marking Scheme:

  • Part (i) correct = 1 mark

  • Part (ii) correct = 1 mark

Q10. Find coordinates of point P. [2]

Distance from x-axis = 5 units downward

y-coordinate = -5

Distance from y-axis = 3 units left

x-coordinate = -3

Therefore,

Coordinates of P = (-3, -5)

Marking Scheme:

  • Correct x-coordinate = 1 mark

  • Correct ordered pair = 1 mark

Q11. Define Cartesian plane. [2]

A Cartesian plane is a flat surface formed by two number lines intersecting at right angles.

  • Horizontal line = x-axis

  • Vertical line = y-axis

  • Four regions formed = Quadrants I, II, III and IV

Marking Scheme:

  • Definition = 1 mark

  • Naming axes and quadrants = 1 mark

SECTION C (6 MARKS)

Q12. Find the fourth vertex of rectangle. [3]

Given:

O(0, 0), A(5, 0), C(0, 3)

Since rectangle sides are parallel to axes:

x-coordinate of B = x-coordinate of A = 5

y-coordinate of B = y-coordinate of C = 3

Therefore,

B = (5, 3)

Justification:
Opposite sides of a rectangle are parallel and equal.

Marking Scheme:

  • Understanding coordinate relation = 1 mark

  • Correct coordinates = 1 mark

  • Proper justification = 1 mark

Q13. Find lengths of PQ and PR. [3]

Given:

P(-1, 2)

Q(3, 2)

R(-1, -2)

Length of PQ

Since y-coordinate is same:

PQ = |3 - (-1)|

= 4 units

Length of PR

Since x-coordinate is same:

PR = |2 - (-2)|

= 4 units

Answer:
PQ = 4 units

PR = 4 units

Marking Scheme:

  • Correct method for PQ = 1 mark

  • Correct method for PR = 1 mark

  • Final answers = 1 mark

SECTION D (5 MARKS)

Q14. Based on K(-3, 2), L(4, 5), M(2, -3), N(-5, -4) [5]

(i)

Abscissa of K = -3

Ordinate of M = -3

(ii)

(Abscissa of L) - (Abscissa of N)

= 4 - (-5)

= 9

(iii)

(Ordinate of K) + (Ordinate of N)

= 2 + (-4)

= -2

Marking Scheme:

  • Part (i) = 2 marks

  • Part (ii) = 1.5 marks

  • Part (iii) = 1.5 marks

SECTION E (4 MARKS)

Q15. Case Study Based Question [4]

Given:

F(3, 4)

P(-4, 2)

G(5, -3)

(i) Quadrants of P and G [1]

P(-4, 2) → Quadrant II

G(5, -3) → Quadrant IV

(ii) Coordinates of cafeteria [1]

Abscissa from P = -4

Ordinate from F = 4

Coordinates = (-4, 4)

(iii) Total perpendicular distance of F from axes [2]

Distance from x-axis = |4| = 4 units

Distance from y-axis = |3| = 3 units

Total distance

= 4 + 3

= 7 units

Marking Scheme:

  • Correct distances = 1 mark

  • Correct total = 1 mark

TOTAL = 30 MARKS

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