On a coordinate plane, a square and a point are shown. The square has points R prime (negative 8, 1), S prime (negative 4, 1), T prime (negative 4, negative 3), and U prime (negative 8, negative 3). Point S is at (3, negative 5). Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has coordinates of (3, –5), which point lies on a side of the pre-image, square RSTU?

(–5, –3)
(3, –3)
(–1, –6)
(4, –9)

45º
90º
180º
270º

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

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

yes.. it's proven to be 36.