CAT Questions | CAT Coordinate Geometry Questions

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?
   
   A. 2
   
   B. 3
   
   C. 5
   
   D. 4
   
   

   Correct Answer

   Choice 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?
   
   A.
   
   B.
   
   C.
   
   D.
   
   

   Correct Answer

   Choice A
   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?
   
   A. 84
   
   B. 92
   
   C. 105
   
   D. 72
   
   

   Correct Answer

   Choice 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?
   
   A. x + y = –1
   
   B. x – y = –1
   
   C. x + y = 1
   
   D. –x + y = –1
   
   

   Correct Answer

   Choice C
   x + y = 1

   Explanation
   

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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?
   
   A. 5 sq units
   
   B. 2.5 sq units
   
   C. 10 sq units
   
   D. 7 sq units
   
   

   Correct Answer

   Choice B
   2.5 sq units

   Explanation

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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?
   
   A. 25π
   
   B. 25
   
   C. 25
   
   D. None of these
   
   

   Correct Answer

   Choice C
   25^π⁄₂

   Explanation

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