Question

6In AABC, AB = x, BC = y, and CA = 2x. A similarity transformation with a scale factor of 0.5 maps AABC to AMNO, such that vertices M, N, and Ocorrespond to A B, and C, respectively. If OM=5, what is AB?OA AB=2.5OB. AB=10OC AB=5OD. AB=1.25OE AB=2

Answer 1

Triangle ABC is scaled to triangle MNO with a scale factor of 0.5.

The lengths of triangle ABC are:

AB = x

BC = y

CA = 2x

The corresponding lengths of triangle MNO are:

MN = 0.5 AB = 0.5x

NO = 0.5 BC = 0.5y

OM = 0.5 CA = 0.5 (2x) = x

We are given OM = 5, thus:

x = 5

Length of AB is x, thus:

AB = 5

Answer: C AB = 5