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CAT Questions | CAT Coordinate Geometry Questions

CAT Quantitative Aptitude | CAT Coordinate Geometry

A CAT Coordinate Geometry question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Graphical Representation of Geometrical shapes, Distance between points, Section formula, Intercepts, Circles and so on. In CAT Exam, one can generally expect to get approx. 1 question from CAT Geometry: Coordinate Geometry. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

CAT Coordinate Geometry: Integer coordinates

Set S contains points whose abscissa and ordinate are both natural numbers. Point P, an element in set S has the property that the sum of the distances from point P to the point (3,0) and the point (0,5) is the lowest among all elements in set S. What is the sum of abscissa and ordinate of point P?
1. 2
2. 3
3. 5
4. 4
Choice D
4
CAT Coordinate Geometry: Geometric Probability

Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?
1. \\frac{1}{4}\\)
2. \\frac{1}{3}\\)
3. \\frac{1}{5}\\)
4. \\frac{1}{2}\\)
Choice A
\\frac{1}{4}\\)
CAT Coordinate Geometry: Greatest integer function

Region Q is defined by the equation 2x + y < 40. How many points (r, s) exist such that r is a natural number and s is a multiple of r?
1. 84
2. 92
3. 105
4. 72
Choice B
92
CAT Coordinate Geometry: Points equidistant from lines

What is the equation of a set of points equidistant from the lines y = 5 and x = –4?
1. x + y = –1
2. x – y = –1
3. x + y = 1
4. –x + y = –1
Choice C
x + y = 1
CAT Coordinate Geometry: Area under curve

What is the area enclosed in the region defined by y = |x – 1| + 2, line x = 1, X–axis and Y–axis?
1. 5 sq units
2. 2.5 sq units
3. 10 sq units
4. 7 sq units
Choice B
2.5 sq units
CAT Coordinate Geometry: Circle and chord

Find the area of the region that comprises all points that satisfy the two conditions x² + y² + 6x + 8y ≤ 0 and 4x ≥ 3y?
1. 25π
2. 25\\frac{π}{4}\\)
3. 25\\frac{π}{2}\\)
4. None of these
Choice C
25\\frac{π}{2}\\)

The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.

CAT 2023 Slot 2 - QA

The area of the quadrilateral bounded by the \(Y\)-axis, the line \(x=5\), and the lines \(|x-y|-|x-5|=2\), is
45
CAT 2023 Slot 1 - QA

Let \(\mathrm{C}\) be the circle \(x^2+y^2+4 x-6 y-3=0\) and \(\mathrm{L}\) be the locus of the point of intersection of a pair of tangents to \(\mathrm{C}\) with the angle between the two tangents equal to \(60^{\circ}\). Then, the point at which \(L\) touches the line \(x=6\) is
1. (6,4)
2. (6,8)
3. (6,3)
4. (6,6)
Choice C
(6,3)
CAT 2022 Slot 1 - QA

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
1. (−4, 5)
2. (4, 5)
3. (−3, 4)
4. (0, 11)
Choice A
(−4, 5)
CAT 2020 Question Paper Slot 3 - Co-ordinate Geometry

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is
1. \\frac{14π}{3})
2. \\frac{123π}{7})
3. \\frac{205π}{9})
4. \\frac{12π}{5})
CAT 2020 Question Paper Slot 3 - Co-ordinate Geometry

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
1. 12
2. 8
3. 6
4. 10
CAT 2020 Question Paper Slot 3 - Co-ordinate Geometry

The points (2 , 1) and (-3 , -4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is
1. 15
2. 13
3. 14
4. 12
CAT 2020 Question Paper Slot 1 - Co-ordinate Geometry

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

Correct Answer: 3
CAT 2019 Question Paper Slot 1 - Coordinate Geometry

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]
3920
CAT 2019 Question Paper Slot 1 - Coordinate Geometry

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]
9
CAT 2019 Question Paper Slot 1 - Coordinate Geometry

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]
2
CAT 2018 Question Paper Slot 2 - Coordinate Geometry

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
1. 4√2 units
2. 2√2 units
3. 4 units
4. 8 units
Choice C
4 units
CAT 2017 Question Paper Slot 2 - Co-ordinate Geometry

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
1. - 5
2. - 6
3. - 7
4. - 8
Choice D
- 8
CAT 2017 Question Paper Slot 1 – Co-ordinate Geometry

The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
1. 4π
2. 4
3. 8
4. 2π
Choice C
8
CAT 2017 Question Paper Slot 1 - Co-ordinate Geometry

The shortest distance of the point (\\frac{1}{2}),1) from the curve y = |x - 1| + |x + 1| is
1. 1
2. 0
3. √2
4. √\\frac{3}{2})
Choice A
1

The Questions that follow, are from actual XAT papers. If you wish to take them separately or plan to solve actual XAT papers at a later point in time, It would be a good idea to stop here.

XAT 2019 Question Paper - QADI
Let P be the point of intersection of the lines 3x + 4y = 2a and 7x + 2y = 2018 and Q the point of intersection of the lines 3x + 4y = 2018 and 5x + 3y = 1 If the line through P and Q has slope 2, the value of a is:
1. 4035
2. ½
3. 3026
4. 1
5. 1009
Choice C
3026
XAT 2019 Question Paper - QADI
Let C be a circle of √20 radius cm. Let L1, L2 be the lines given by 2x − y −1 = 0 and x + 2y−18 = 0, respectively. Suppose that L1 passes through the center of C and that L2 is tangent to C at the point of intersection of L1 and L2. If (a,b) is the center of C, which of the following is a possible value of a + b?
1. 11
2. 17
3. 8
4. 20
5. 14
Choice B
17

The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.

IPMAT 2020 Question Paper - IPM Indore Quants
The shortest distance from the point (-4,3) to the circle x² + y² = 1 is __________.
4
IPMAT 2020 Question Paper - IPM Indore Quants
The equation of the straight line passing through the point M (-5,1), such that the portion of it between the axes is divided by the point M in to two equal halves, is
1. 10y - 8x = 80
2. 8y + 10x = 80
3. 10y + 8x = 80
4. 8y + 10x + 80 = 0
Choice A
10y - 8x = 80
IPMAT 2019 Question Paper - IPM Indore Quants
The circle x² + y² - 6x - 10y + k = 0 does not touch or intersect the coordinate axes. If the point (1, 4) does not lie outside the circle, and the range of k is (a, b] then a + b is
54
IPMAT 2019 Question Paper - IPM Indore Quants
The area enclosed by the curve 2|x| + 3|y| = 6 is
1. 12 square units
2. 3 square units
3. 4 square units
4. 24 square units
Choice A
12 square units
IPMAT 2019 Question Paper - IPM Indore Quants
The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 31), and (31, 0) is
1. 435
2. 465
3. 450
4. 464
Choice A
435