Question

A dilation maps APQR onto △ P'Q'R Find the missing values

PQ=5 h P'Q'=40 in
QR=3in Q'R'= _ in
PR=6in P'R'= _ in

PQ=5in P'Q'=40 in
QR=3m Q'R'=
PR=6in P'R'= in (Simplify your answers.)

Answer 1

To find the missing lengths Q'R' and P'R' after a dilation with a scale factor of 8, multiply the original lengths QR and PR by 8, resulting in Q'R' = 24 inches and P'R' = 48 inches.

Step-by-step explanation:

The student is trying to find missing lengths in a pair of similar triangles where one is a dilation of the other. The given lengths are PQ = 5 inches and P'Q' = 40 inches, meaning the scale factor is 40 inches / 5 inches = 8. To find Q'R' and P'R', we multiply the original lengths of QR and PR by the scale factor of 8.

For QR = 3 inches:
Q'R' = QR × scale factor = 3 inches × 8 = 24 inches.

For PR = 6 inches:
P'R' = PR × scale factor = 6 inches × 8 = 48 inches.