In ΔEKF, points G and H are located on sides EK and FK such that GH is parallel to EF. Which dilation will map ΔGKH on ΔEKF? Show your work. (1) a dilation by a factor of 5/3 centered at K
(2) a dilation by a factor of 3/2 centered at K
(3) a dilation by a factor of 5/3 centered at G
(4) a dilation by a factor of 3/2 centered at G

is should be y = 5x

step-by-step explanation:

correct me if im wrong

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