Are the lines x – 2y = 4 and y = 2x – 2

a. perpendicular
b. parallel
c. or neither

C

Step-by-step explanation:

x - 2y = 4

-2y = -x + 4

y = 1/2x - 2

y = 2x - 2

Almost perpendixular but not quite. Parallel lines must have the same slope. Therefore, it's neither

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4