Set S contains points whose abscissa and ordinate are both natural numbers Point P an element in set...........

Quantitative Aptitude ( CCS) Coordinate Geometry

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?

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Explanation:

Any point on the line x/3 + 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

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