Question

Identify the scale factor used to graph the image below

Answer 1

Answer:

$Scale = \frac{2}{3}$

Step-by-step explanation:

To solve this question, I'll use the coordinates of SV and S'V' as points of reference.

From the attachment:

$S = (3,6)$

$V = (15,3)$

$S' = (2,4)$

$V' = (10,2)$

First, calculate distance SV

Distance formula is:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

For SV:

$d_1 = \sqrt{(15 - 3)^2 + (3 - 6)^2}$

$d_1 = \sqrt{(12)^2 + (-3)^2}$

$d_1 = \sqrt{144 + 9}$

$d_1 = \sqrt{153}$

For S'V'

$d_2 = \sqrt{(10 - 2)^2 + (2 - 4)^2}$

$d_2 = \sqrt{64 + 4}$

$d_2 = \sqrt{68}$

The scale factor is then calculated using:

$Scale = \frac{S'V'}{SV}$

$Scale = \frac{d_2}{d_1}$

Substitute values of d1 and d2

$Scale = \frac{\sqrt{68}}{\sqrt{153}}$

$Scale = \sqrt{\frac{68}{153}}$

$Scale = \sqrt{\frac{1}{2.25}}$

$Scale = \frac{1}{1.5}$

Express as a proper fraction

$Scale = \frac{1*2}{1.5*2}$

$Scale = \frac{2}{3}$