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.

  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
    Choice D
    4

  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}\\)
    Choice A
    \\frac{1}{4}\\)

  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
    Choice B
    92

  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
    Choice C
    x + y = 1

  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
    Choice B
    2.5 sq units

  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
    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.


  1. 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
    Choice D
    10

  2. 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})
    Choice C
    \\frac{205π}{9})

  3. 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
    Choice C
    14

  4. 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


  5. 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

    1. 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]


    2. 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]


    3. 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

    4. 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

    5. 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. 4
      2. 8
      Choice C
      8

    6. 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.


    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
      Choice C
      3026

    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
      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.


    1. IPMAT 2020 Question Paper - IPM Indore Quants

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

      4

    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
      Choice A
      10y - 8x = 80

    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


    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
      Choice A
      12 square units

    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
      Choice A
      435


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