Question

in Δ ABC, AB=x, BC=y, and CA=2x. A similarity transformation with a scale factor of 0.5 maps Δ ABC to Δ MNO, such that vertices M, N, and O correspond to A, B, and C, respectively. If OM=5, what is AB?

Answer 1

A. AB=2.5
B. AB= 10
C. AB= 5
D. AB= 1.25
E. AB= 2

Answer 2

corresponding sides would be in the ratio 1:0.5 withe MNO being smallest triangle.
which side in triangle ABC corresponds to OM in triangle MNO?

Answer 3

Side CA I believe @welshfella

Answer 4

thats correct

Answer 5

so OM = 0.5*CA
and CA = 2x
so OM = 0.5* 2x
also OM = 5
so 5 = 0.5* 2x

can you continue?

Answer 6

do you follow that OK?

Answer 7

each of the sides in MNO are 1/2 length of corresponding sides in ABC - because the scale factor is 0.5.

Answer 8

Now as AB = x if you solve the equation for x that's the length of AB.

Answer 9

I believe so I had to think a bit after that but if I did it right wouldn't AB =5? @welshfella

Answer 10

yes x = 5
so AB = 5

Answer 11

Okay thanks for the help @welshfella