Question

The angle from the line through (-4, 5) and (3, y) to the line through (-2, 4) and (9, 1) is 135º. Find y.

Answer 1

recall that if slope of line1 = m1 and the slope of line2 = m2
then if β is the angle between them, then
tan β = (m1 - m2)/(1 + m1m2)

slope of line1 = (y-5)/7, slope of line2 = -3/11
and tan 135 = -1
we have:
-1 = ( (y-5)/7 + 3/11)/(1 - (3/11)(y-5)/7 )
(y-5)/7 + 3/11 = -1 + (3/77)(y-5)
times 77
11(y-5) + 21 = -77 + 3y -15
11y - 55 + 21 = -77 + 3y - 15
8y = -58
y = -29/4

make a sketch to see that this is correct