CAT Practice : 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.

Straightline Shortest distance

    Q.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


  • Correct Answer
    Choice D. 4

Detailed Solution

Any point on the line = 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) =
Sum of distances for (1, 3) =
Sum of distances for (2, 1) =
Sum of distances for (2, 2) =

is the shortest distance.
Sum of abscissa + ordinate = 4

Correct Answer: 4

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More questions from Coordinate Geometry

  1. Straightline Shortest distance
  2. Coordinate Geometry and Probability
  3. Cogeo and greatest integer function
  4. Angle bisector theorem
  5. Area under curve
  6. Area of segment
Take Geometry, add one unit of algebra; take a diagram, explain it with x's and y's. For the purists, it is geometry without the romance, for the pragmatists it is Geometry with expanded scope.