CAT 2020: Coordinate Geometry | Additional Study Material for CAT PDF Download

Q.1. The area of the region satisfying the inequalities | x | - y ≤ 1, y ≥ 0 and y ≤ 1 is

Ans: 3
The graph of | x | - y ≤ 1, y ≥ 0 and y ≤ 1 is as follows:
Area of ABCD = Area of EFCD - Area of EAD - Area of BFC
=
=
= 4 - 1 = 3 Square units.

Q.2. The area, in sq. units, enclosed by the lines x = 2, y =| x - 2 | + 4 , the X -axis and the Y -axis is equal to
(a) 8
(b) 12
(c) 10
(d) 6

Correct Option is C
The line y =| x - 2 | + 4 intersects the y -axis at (0,6) and intersects x = 2 at (2, 4)
The other vertices are (0,0) and (2,0)
The figure formed is a trapezium of parallel sides 6 and 4 and the distance between the parallel sides is 2.
Required answer = 1/2 x 2 x (6 + 4) = 10 

Q.3. The vertices of a triangle are (0,0),(4,0) and (3,9). The area of the circle passing through these three points is
(a) 14π/3
(b) 12π/5
(c) 123π/7
(d) 205π/9

Correct Option is D

Area of the triangle = 1/2 x 4 x 9 = 18
The circumradius of the triangle
Area of the circle
=
=

Q.4. The points (2,1) and (-3,-4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x + 9 y + c = 0 , then c is
(a) 12
(b) 14
(c) 13
(d) 15

Correct Option is B
The given line also passes through the point of intersection of the diagonals of the parallelogram, which is the mid-point of (2,1) and (-3,-4) The mid-point of the given two points is (-1/2, -3/2).
Substituting the point in the given equation
⇒ c = 14