CAT Questions | CAT Coordinate Geometry Questions

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.

1. 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

   Correct AnswerChoice D
   4

   Explanation

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2. 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}\\)

   Correct AnswerChoice A
   \\frac{1}{4}\\)

   Explanation

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3. 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

   Correct AnswerChoice B
   92

   Explanation

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4. 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

   Correct AnswerChoice C
   x + y = 1

   Explanation Video Solution

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5. 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

   Correct AnswerChoice B
   2.5 sq units

   Explanation Video Solution

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6. 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

   Correct AnswerChoice C
   25\\frac{π}{2}\\)

   Explanation Video Solution

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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.

1. 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)

   Correct AnswerChoice A
   (−4, 5)

   Video ExplanationExplanation

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2. 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

   Correct AnswerChoice D
   10

   Video SolutionExplanation

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3. 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})

   Correct AnswerChoice C
   \\frac{205π}{9})

   Video SolutionExplanation

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4. 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

   Correct AnswerChoice C
   14

   Video SolutionExplanation

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5. 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 Answer3
   

   Video SolutionExplanation

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6. 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]

   Correct Answer3920
   

   ExplanationVideo Solution

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7. 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]

   Correct Answer9
   

   ExplanationVideo Solution

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8. 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]

   Correct Answer2
   

   ExplanationVideo Solution

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9. 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

   Correct AnswerChoice C
   4 units

   ExplanationVideo Solution

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10. 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

    Correct AnswerChoice D
    - 8

    ExplanationVideo Solution

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11. 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

    Correct AnswerChoice C
    8

    ExplanationVideo Solution

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12. 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})

    Correct AnswerChoice A
    1

    ExplanationVideo Solution

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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.

1. 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

   Correct AnswerChoice C
   3026

   Video SolutionExplanation

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2. 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

   Correct AnswerChoice B
   17

   Video SolutionExplanation

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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.

1. IPMAT 2020 Question Paper - IPM Indore Quants

   The shortest distance from the point (-4,3) to the circle x² + y² = 1 is __________.

   Correct Answer4
   

   Explanation

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2. 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

   Correct AnswerChoice A
   10y - 8x = 80

   Explanation

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3. 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

   Correct Answer54

   ExplanationVideo Solution

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4. 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

   Correct AnswerChoice A
   12 square units

   ExplanationVideo Solution

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5. 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

   Correct AnswerChoice A
   435

   ExplanationVideo Solution

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