CAT MCQs on Coordinate Geometry: CAT Questions for Practice with Solutions

The CAT QA section requires speed and accuracy, along with a thorough understanding of the Coordinate Geometry. This article provides a set of MCQs on Coordinate Geometry to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation

Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.

The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.

CAT MCQs on Coordinate Geometry

1. Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4), and (−2, 8), respectively. Then, the coordinates of the vertex D are

A

(−4, 5)

B

(4, 5) 

C

(−3, 4)

D

(0, 11) 

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2. In the XY-plane, the area, in sq. units, of the region defined by the inequalities y ≥ x + 4 and −4 ≤ x² + y² + 4(x − y) ≤ 0 is

A

\(2\pi\)

B

\(3\pi\)

C

\(\pi\)

D

\(4\pi\)

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3. In the figure below, \( \angle MON = \angle MPO = \angle NQO = 90^\circ \), \( OQ \) is the bisector of \( \angle MON \), and \( QN = 10 \), \( OR = 40/\sqrt{7} \). Find \( OP \).

A

4.8

B

4.5

C

4

D

5

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4. In the figure, \( OABC \) is a parallelogram. The area of the parallelogram is 21. Coordinates are: \( O = (0,0) \), \( A = (7,0) \), and point \( C \) lies on line \( x = 3 \). Find coordinates of \( B \).

A

(3, 10)

B

(10, 3)

C

(10, 10)

D

(8, 3)

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5. ABCD is a rectangle. Points \( P \) and \( Q \) lie on \( AD \) and \( AB \) respectively. If triangles \( PAQ, QBC, \) and \( PCD \) all have the same areas and \( BQ = 2 \), then \( AQ = \) ?

A

\( 1 + \sqrt{5} \)

B

\( 1 - \sqrt{5} \)

C

\( \sqrt{7} \)

D

\( 2\sqrt{7} \)

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6. A rectangle has a perimeter of 50 cm and an area of 150 cm². Find its length.

A

15 cm

B

10 cm

C

20 cm

D

25 cm

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7. Find the distance between points (2, 3) and (5, 7).

A

4

B

5

C

6

D

7

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8. The sum of the first n natural numbers is 55. What is n? 

 

A

8

B

9

C

10

D

11

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9. ABCD is a rhombus with AC and BD intersecting at the origin. The equation of side AD is x + y = 1. What is the equation of BC?

A

x + y = 1

B

x + y = -1

C

x - y = 1

D

x - y = -1

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10. Find the area bounded by the curves |x + y| = 1, |x| = 1, |y| = 1.

A

4

B

3

C

2

D

1

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11. ABC is an equilateral triangle with AB = AC, and B is 2 km north of A. A person walks from B parallel to AC, stops when directly east of C (point D). Where is D with respect to A?

A

3 km east and 1 km north of A

B

3 km east and \( \sqrt{3} \) km north of A

C

\( \sqrt{3} \) km east and 1 km south of A

D

\( \sqrt{3} \) km west and 3 km north of A

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12. What is the total distance walked by the person (from B to D to E)?

A

3 km

B

4 km

C

\( 2\sqrt{3} \) km

D

6 km

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13. A slab of ice 8 in × 11 in × 2 in is melted and recast into a cylinder of 8 in diameter. What is the length of the cylinder?

A

3

B

3.5

C

4

D

4.5

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14. From 5 points (4 vertices of a square + 1 intersection point of diagonals), how many triangles can be formed?

A

4

B

6

C

8

D

10

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15. What is the distance between the points A(3, 8) and B(-2, -7)?

A

\( 5\sqrt{2} \)

B

5

C

\( 5\sqrt{10} \)

D

\( 10\sqrt{2} \)

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