1. Draw, in BLACK, the triangle with vertices (–1,5), (-6, 3), and (-4,8). 2. In BLUE, draw the triangle when the BLACK triangle is translated by the function (x, y) = (x, y - 6).
3. In GREEN, draw the triangle when the BLACK triangle is reflected in the y-axis.

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y

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