# Question 59ae1

Sep 8, 2017

0.5

#### Explanation:

...which you can arrive at with one calculation - namely the ratio of the delta-x coordinates of the two polygons

$\delta {x}_{1} = 8 - 0 = 8$
$\delta {x}_{2} = 2 - 6 = - 4$

...we're just concerned with magnitudes here, so we'll ignore the negative sign in the delta x for the second polygon. The magnitude of this difference is 4.

The ratio of these is the scale factor. $8 \cdot x = 4$, so x = 4/8 = 0.5.

This is the same ratio as that for the corresponding sides of the 2 polygons.

I.e, the length of AB: sqrt((8-0)^2 + (8 - (-7))^2 = 17

length of A'B' = sqrt((2 - 6)^2 + (1.5 - (-6))^2# = 8.5

...and 8.5/17 = 0.5, your scale factor. Doing it the second way, using the pythagorean theorem, is just a few more calculations.