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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?
2
3
5
4
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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