CAT Practice : Coordinate Geometry

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The following topics are covered in the CAT quant section from Geometry - Coordinate Geometry. Detailed explanatory answers, solution videos and slide decks are also provided.
  1. Straightline Shortest distance

    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
  2. Coordinate Geometry and 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?

    • Correct AnswerChoice (A).
      Correct answer
    • Explanatory Answer
    • Geometric Probability
    • Hard
  3. Coordinate geometry and 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
  4. Angle bisector theorem

    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
      Correct answer
    • Explanatory Answer
    • Points equidistant from lines
    • Hard
  5. 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
      Correct answer
    • Explanatory Answer
    • Modulus graph
    • Medium
  6. Area of segment

    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. None of these
    • Correct AnswerChoice (C).
      Correct answer
    • Explanatory Answer
    • Circle and chord
    • Hard

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