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CAT Exam  >  CAT Test  >  Level-wise Tests  >  Test Level 2: Coordinate Geometry - 1 - CAT MCQ

Test Level 2: Coordinate Geometry - 1 Solved MCQs CAT


MCQ Practice Test & Solutions: Test Level 2: Coordinate Geometry - 1 (10 Questions)

You can prepare effectively for CAT Level-wise Tests for CAT with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test Level 2: Coordinate Geometry - 1". These 10 questions have been designed by the experts with the latest curriculum of CAT 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 10

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Test Level 2: Coordinate Geometry - 1 - Question 1
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The following points A (2a, 4a), B (2a, 6a) and C (2a +√3a, 5a) (a > 0) are the vertices of

Detailed Solution: Question 1



Since AB = BC = CA, hence triangle is equilateral. Therefore, it is an acute angled triangle.

Test Level 2: Coordinate Geometry - 1 - Question 2
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In the rectangle shown below, the value of a - b is

Detailed Solution: Question 2

To go from the point (5, 5) to the point (9, 2), we must move over to the right by 4 units and down by 3 units.
Since we are dealing with a rectangle, the same must be true for (a, 13) and (15, b).
Thus, a + 4 = 15 and 13 - 3 = b.
From this, a = 11 and b = 10.
So a - b = 11 - 10 = 1.

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Test Level 2: Coordinate Geometry - 1 - Question 3
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A straight line passing through the point of intersection of the straight lines x - 3y + 1 = 0 and 2x + 5y - 9 = 0 having infinite slope and at a distance of 2 units from the origin, has the equation  

Detailed Solution: Question 3

The intersection point of x - 3y + 1 = 0 and 2x + 5y - 9 = 0 is (2, 1).
And, m = 1/0.
So, the required line is y - 1 = (1/0)(x - 2)
⇒ x = 2.

Test Level 2: Coordinate Geometry - 1 - Question 4
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The equation of the line, which passes through the point (1, -2) and cuts off equal intercepts from the axis, is  

Detailed Solution: Question 4

Intercept form of line = x/y + y/b = 1
In case of equal intercepts, a = b
Therefore, 

 As it passes through (1, - 2),
⇒ 1 - 2 = a, a = -1
The equation of line is x + y + 1 = 0.

Test Level 2: Coordinate Geometry - 1 - Question 5
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A line intersects x-axis at A(10, 0) and y-axis at B(0, 10). Find the equation of the line.  

Detailed Solution: Question 5

As line intersects x-axis at A (10, 0)
Length of intercept on x-axis, a = 10
Similarly length of intercept on y-axis, b = 10
∴ Using intercept form, equation of line is x/10 + y/10 = 1
or x + y = 10.

Test Level 2: Coordinate Geometry - 1 - Question 6
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The equation of the line passing through the point of intersection of the lines 4x - 3y - 1 = 0 and 5x - 2y - 3 = 0 and parallel to the line 2y - 3x + 2 = 0, is

Detailed Solution: Question 6

The point of intersection of the lines 4x - 3y - 1 = 0 and 5x - 2y - 3 = 0 is (1, 1).
The equation of line parallel to 2y - 3x + 2 = 0 is 2y - 3x + k = 0.
It also passes through (1, 1), so k = 1.
Hence, the required equation is 2y - 3x + 1 = 0 or 3x - 2y = 1.

Test Level 2: Coordinate Geometry - 1 - Question 7
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The coordinates of four points are P(0, -3), Q(6, 1), R(-4, -4) and S(5, 2). Find out which line segments are parallel to each other.

Detailed Solution: Question 7

Slope of PQ: [1 - (-3)]/[6 - 0] = 2/3 
Slope of RS: [2 - (-4)]/[5 - (-4)] = 2/3
Since the slopes of the two lines are equal, the lines are parallel. 

Test Level 2: Coordinate Geometry - 1 - Question 8
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Line m is the graph of the equation 2x + 3y = 7. If the point at which m crosses the y-axis has coordinates (0, k), what is the value of k?

Detailed Solution: Question 8

The equation of the y-axis is x = 0.
So, the line 2x + 3y = 7 will cut the y-axis at the point 3y = 7, or y = 7/3.
So, k = 7/3, or 

Test Level 2: Coordinate Geometry - 1 - Question 9
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The area of the circle in which a chord of length √2 makes an angle π/2 at the centre is  

Detailed Solution: Question 9



where r = radius = 1 unit
Area = πr2 = π12 = π

Test Level 2: Coordinate Geometry - 1 - Question 10
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Find the value of k, for the three lines x + y - 4 = 0, 3x + 2 = 0 and x - y + 3k = 0 to be concurrent

Detailed Solution: Question 10


1(0 + 2) - 1 (9k - 2) - 4 (-3 - 0) = 0
9k = 16
or k = 16/9

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About this CAT Practice Test

This test contains 10 MCQs on Test Level 2: Coordinate Geometry - 1 with detailed solutions for each question. It is part of the Level-wise Tests for CAT course on EduRev, designed to align with the current CAT syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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