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?

1. ${1 \over 4}$
2. ${1 \over 3}$
3. ${1 \over 5}$
4. ${1 \over 2}$
• Correct AnswerChoice (A).
${1 \over 4}$
• 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
• 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
• 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. ${25{\pi} \over 4}$
3. ${25{\pi} \over 2}$
4. None of these
• Correct AnswerChoice (C).
${25{\pi} \over 2}$