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

Test Level 2: Coordinate Geometry - 1 - CAT MCQ


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10 Questions MCQ Test - Test Level 2: Coordinate Geometry - 1

Test Level 2: Coordinate Geometry - 1 for CAT 2024 is part of CAT preparation. The Test Level 2: Coordinate Geometry - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 2: Coordinate Geometry - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 2: Coordinate Geometry - 1 below.
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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 for Test Level 2: Coordinate Geometry - 1 - 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 for Test Level 2: Coordinate Geometry - 1 - 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 for Test Level 2: Coordinate Geometry - 1 - 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 for Test Level 2: Coordinate Geometry - 1 - 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 for Test Level 2: Coordinate Geometry - 1 - 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 for Test Level 2: Coordinate Geometry - 1 - 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 for Test Level 2: Coordinate Geometry - 1 - 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 for Test Level 2: Coordinate Geometry - 1 - 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 for Test Level 2: Coordinate Geometry - 1 - 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 for Test Level 2: Coordinate Geometry - 1 - Question 10


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

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