The equation of a line through the point (1, 2) whose distance from the point `(3,1)` has the greatest value is `y=2x` (b) `y=x+1` `x+2y=5` (d) `y=3x-1`

Options

A. y=2x
B. y=x+1
C. x+2y=5
D. y=3x-1

Answer

A

Explanation

Obviously, the line through Q is at the greatest distance from point P when it is perpendicular to PQ. Now, the slope of line PQ is `m_(PQ) = -1//2`. Then the slope of perpendicular line passing through Q is
y-2 = 2(x-1)
or 2x-y=0