CAT Quantitative Aptitude Questions | Questions for CAT - Coordinate Geometry

CAT Questions | CAT Coordinate Geometry | Integer Coordinates

The question is from CAT Coordinate Geometry. This is about Integer Coordinates. We need to find out the sum of abscissa and ordinate of a particular given point. Open-ended questions that ask us to find points that are closest to a line or farthest from an arc are the toughest. It is important to find the best starting point in these kinds of questions. CAT exam does test one on ideas from CAT Coordinate Geometry once in a while.

Question 1: 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

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Explanatory Answer

Method of solving this CAT Question from CAT Coordinate Geometry : Open-ended questions that ask us to find points that are closest to a line or farthest from an arc are the toughest. It is important to find the best starting point in these kinds of questions.

Any point on the line \\frac{x}{3}\\) + \\frac{y}{5}\\) = 1 will have the shortest overall distance. However, we need to have integral coordinates. So, we need to find points with integral coordinates as close as possible to the line 5x + 3y = 15.
Substitute x =1, we get y = 2 or 3
Substitute x = 2, we get y = 1 or 2

Sum of distances for (1, 2) = √8 + √10
Sum of distances for (1, 3) = √13 + √5
Sum of distances for (2, 1) = √2 + √20
Sum of distances for (2, 2) = √5 + √13
√5 + √13 is the shortest distance.
Sum of abscissa + ordinate = 4

The question is "What is the sum of abscissa and ordinate of point P?"

Hence, the answer is 4.

Choice D is the correct answer.

 

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