equation of straight line,perpendicular to the straight line

Question

find the equationof the straight line passing through A[-1,3] and perpendicular to the straight line passing through B[2,-5] and C[4,6].

Answer 1

use b and c first

b(2, -5), c(4, 6)

M = (Yb - Yc)/(Xb - Xc)

M = (-5 - 6) / (2 - 4)

M = -11/-2 = 11/2

I choose 'b' to get the equation

y + 5 = 11/2(x - 2)

y + 5 = 11/2x - 22/2

y = 11/2x - 11 - 5

y = 11/2x - 16

the slope of the perpendicular line is the negative reciprical.

M of original line is 11/2 negative reciprical is

-2/11 and use the point c(-1, 3)

y - 3 = -2/11(x + 1)

y - 3 = -2/11x - 2/11

y = -2/11x - 2/11 + 3

y = -2/11x + 31/11 is the perpendicular line