Let `A(3,4)` and `B(5,8)`be two points. If `C` is a point on the x-axis such that `AC+BC` is minimum then the co ordinates of `C` are

Options

A. (5/3 , 0)
B. (1/3 , 0)
C. (3,0)
D. none of these

Explanation

Clearly , AC + BC , will be minimum when points B , C and D (image of A in x-axis ) are collinear . In that case C is the intersection of BD with x-axis .

The equation of BD is
`y + 1 = (2 +1)/(3 -1) (x -1) implies 3x - 2y - 5 = 0`
It cuts x-axis at (5/3 , 0) .
Hence, the coordinates of the required point are (5/3 , 0)