Question

identify the center of dilation and scale factor of each dilation.
6.
7.

Explanation:

Step1: Find center for Figure 6

Connect corresponding points (e.g., $B$ to $B'$, $D$ to $D'$) with straight lines. The intersection of these lines is the center of dilation, located at $(0, 0)$ (the origin of the grid).

Step2: Calculate scale factor for Figure 6

Measure distance from center to a point and its image. For point $B$: distance from $(0,0)$ to $B$ is 2 units up; distance to $B'$ is 4 units up. Scale factor $k = \frac{\text{length of } OB'}{\text{length of } OB} = \frac{4}{2} = 2$.

Step3: Find center for Figure 7

Connect corresponding points (e.g., $K$ to $K'$, $M$ to $M'$) with straight lines. The intersection of these lines is the center of dilation, located at $(0, 0)$ (the origin of the grid).

Step4: Calculate scale factor for Figure 7

Measure distance from center to a point and its image. For point $K$: distance from $(0,0)$ to $K$ is 6 units right, 4 units up; distance to $K'$ is 3 units right, 2 units up. Scale factor $k = \frac{\text{length of } OK'}{\text{length of } OK} = \frac{1}{2}$.

Answer:

For Figure 6:

Center of dilation: $(0, 0)$; Scale factor: $2$

For Figure 7:

Center of dilation: $(0, 0)$; Scale factor: $\frac{1}{2}$