Question

1. identify the scale factor used to graph the image below.

Explanation:

Step1: Select a corresponding side

Choose side $SU$ and $S'U'$. Assume each grid - square side length is 1 unit. The length of $SU$ can be found using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $S$ and $U$, if we assume $S(x_1,y_1)$ and $U(x_2,y_2)$, by counting the grid - squares, $SU=\sqrt{(4 - 2)^2+(6 - 2)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}$. The length of $S'U'$: for points $S'$ and $U'$, $S'U'=\sqrt{(2 - 1)^2+(3 - 1)^2}=\sqrt{1+4}=\sqrt{5}$.

Step2: Calculate the scale factor

The scale factor $k$ from the original figure (with side $SU$) to the new figure (with side $S'U'$) is given by the ratio of the side - length of the new figure to the side - length of the original figure. So $k=\frac{S'U'}{SU}=\frac{\sqrt{5}}{2\sqrt{5}}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$