Triangle J′K′L′ shown on the grid below is a dilation of triangle JKL using the origin as the center of dilation: Two triangles are drawn on a grid. First triangle has vertices J 6 and 12, K 9 and 6, L 12 and 9. Image triangle has vertices J prime 2 and 4, K prime 3 and 2, L prime 4, and 3. Which scale factor was used to create triangle J′K′L′? A. 1 /3 B. 4 C .3 D. 1/4

sine

step-by-step explanation:

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

9x