CAT Previous Year Questions - Coordinate Geometry - Notes | Study Quantitative Aptitude (Quant) - CAT
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Question for CAT Previous Year Questions - Coordinate Geometry
Try yourself:The area of the region satisfying the inequalities | x | - y ≤ 1, y ≥ 0 and y ≤ 1 is
Correct Answer : 3
Explanation
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.
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Question for CAT Previous Year Questions - Coordinate Geometry
Try yourself: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
[2020]
Explanation
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
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Question for CAT Previous Year Questions - Coordinate Geometry
Try yourself:The vertices of a triangle are (0,0),(4,0) and (3,9). The area of the circle passing through these three points is
[2020]
Explanation
Area of the triangle = 1/2 x 4 x 9 = 18 The circumradius of the triangle Area of the circle = =
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Question for CAT Previous Year Questions - Coordinate Geometry
Try yourself: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
[2020]
Explanation
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
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Question for CAT Previous Year Questions - Coordinate Geometry
Try yourself:With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from any point (x,y) is either to (x,y+1) or to (x+1,y) is
[TITA 2019]
Correct Answer : 3920
Explanation
Let us first consider travelling from (1,1) to (4, 6) This means, Travelling from 1 to 4 units in the x axis → 3 horizontal movements (h h h) And travelling from 1 to 6 units in the y axis -> 5 vertical movements (v v v v v) No matter how we proceed, reaching from (1,1) to (4,6) requires 5 vertical movements and 3 horizontal movements. So, Number of paths to travel from (1,1) to (4,6) = Number of ways of arranging (h h h v v v v v) Number of ways of arranging (h h h v v v v v) = Similarly, travelling from (4, 6) to (8, 10) requires 4 horizontal movements and 4 vertical movements Number of ways of arranging (h h h h v v v v) = Total number of paths = x = x = 3920
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Question for CAT Previous Year Questions - Coordinate Geometry
Try yourself:Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is
[TITA 2019]
Correct Answer : 9
Explanation
We know that the equation of the straight line is 3x + 5y = 45
The intercepts are (15,0) and (0,9) respectively Since it's a right-angled triangle, we know that Circumradius (R) = Circumradius = = We know that is approximately equal to 6 So, from trial and error to find the closest number, we find that the value of Circumradius is very close to 9 So, the integer closest to L = 9
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Question for CAT Previous Year Questions - Coordinate Geometry
Try yourself:Let S be the set of all points (x,y) in the x-y plane such that |x| + |y| ≤ 2 and |x| ≥ 1. Then, the area, in square units, of the region represented by S equals
[TITA 2019]
Correct Answer : 2
Explanation
Construct the given data on a rough graph. Required area = Sum of area of two smaller triangles [ (-2,0) (-1,1) (-1,-1) and (2,0) (1,-1) (1,1) ] Required area = 2 x 1/2 x base x height Required area = 1 x 2 = 2 Sq units
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Question for CAT Previous Year Questions - Coordinate Geometry
Try yourself:A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is
[2018]
Explanation
Given Area (△ABC) = 32 sq units and one of the length BC = 8 units on the line x = 4 Let us draw a graph and plot the given values. We know that area of the Triangle = 1/2 × base × height considering BC as the base, area of the Triangle = 1/2 × 8 × height = 32 Height = Since the base lies on x = 4 and has a vertical height is of length = 8 units, A can either lie on the line x = 12 or on x = - 4 However, since we need to find the shortest possible distance between A and the origin, A should lie on the line x = - 4 So, shortest possible distance to A from the point (0,0) = 4 units
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The document CAT Previous Year Questions - Coordinate Geometry - Notes | Study Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).