The equation of a line through the point (1, 2) whose distance from the point(3, 1) has the greatest value, is

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