Right triangle XYZ, with vertex _Y at (-3,0), is rotated clockwise 180° about the origin. Which of the following rotations is equivalent to 180° clockwise rotation about the origin?
counterclockwise 180°
clockwise 270
counterclockwise 360°
clockwise 360°

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