Question

what is the scale factor? give only the number

Explanation:

Step1: Select corresponding side lengths

Let's consider the side - length of the smaller rectangle, say the horizontal side of rectangle $PQON$ from $P$ to $O$. The distance between $P(2,2)$ and $O(2, - 2)$ is $4$ (using the distance formula for points with the same $x$ - coordinate: $d=\vert y_1 - y_2\vert=\vert2-( - 2)\vert = 4$). For the larger rectangle $P'Q'O'N'$, the corresponding horizontal side from $P'(8,8)$ to $O'(8, - 8)$ has a length of $16$ (since $\vert8-( - 8)\vert = 16$).

Step2: Calculate scale factor

The scale factor $k$ is given by the ratio of the side - length of the larger figure to the side - length of the smaller figure. So, $k=\frac{\text{side length of larger figure}}{\text{side length of smaller figure}}=\frac{16}{4}=4$.

Answer:

4