Maria draws ∆PQR. Then she applies a dilation with scale factor 1/3 and center of dilation P to the triangle. Next, she translates the image 2 centimeters up and 3 centimeters right. She labels the final image as ∆XYZ. Which of the following must be true about ∆PQR and ∆XYZ? A. ∆PQR and ∆XYZ are congruent and similar. B. ∆PQR and ∆XYZ are congruent but not similar. C. ∆PQR and ∆XYZ are similar but not congruent. D. ∆PQR and ∆XYZ are neither similar nor congruent. Please help me

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

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