Correct Answer - Option 2 : 4
Calculation:
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 the 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 is 4.