On a coordinate plane, a triangle has points a prime (negative 2, 10), b prime (negative 6, 4), and (negative 10, 8). what is the pre-image of vertex a' if the image shown on the graph was created by a reflection across the line y = x? (10, –2) (–10, 2) (–2, –10) (2, 10)

only 10/60 isn't equivalent

hope this : )

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