Question

Determine whether the figures are similar.

If so, determine the scale factor.

a. yes; scale factor = 4/7
b. yes; scale factor = 1/3
c. yes; scale factor = 2/7
d. no

Answer 1

The answer is c. yes; scale factor = 2/7

The figures are similar if:

`(a_1)/(b_1) = (a_2)/(b_2) \\ \\ a_1b_2 = a_2b_1`

a1 = 4
b1 = 7
a2 = 14
b2 = 24.5


`a_1b_2 = a_2b_1 \\ \\ 4 * 24.5 = 7 * 14 \\ 98 = 98`

The figures are similar, now let's find the scale factor:

`(a_1)/(a_2) = (4)/(14) = (4:2)/(14:2) = (2)/(7) \\ \\ (b_1)/(b_2) = (7)/(24.5) = (7:3.5)/(24.5:3.5) = (2)/(7) \\ \\`