The condition that the line joining P (x, y) and Q(- 3, 1) be perpendicular to the line joining A (4, 6) and B (2, - 5) is (a) 2x + 11y = 8 ( b) 2x + 11y = 5 ( c) 2x - 11y + 17 = 0 (d ) 2x - 11y - 17 = 0
Easiest way:
slope of AB = (6+5)/(4-2) = 11/2
So the slope of the perpendicular must be -2/11
and the equation must be
2x + 11y = c
we know (-3,1) is supposed to lie on it
2(-3) + 11 = c = 5
equation: 2x + 11y = 5
or:
(after finding the slope of AB from above, and deciding
that the new slope must be -2/11
new equation:
y - 1 = (-2/11)(x+3)
times 11
11y - 11 = -2x - 6
2x + 11y = 11-6
2x + 11y = 5