Question

on the coordinate grid, hailey drew figure 1 with vertices (-2, 2), (-2, 6), (-8, 6), and (-8, 2). then she transformed it to produce figure 2 with vertices (5, - 4), (5, - 2), (2, - 2), and (2, - 4). part a figure 1 maps onto figure 2 by a sequence of transformations. describe the sequence of transformations. are figures 1 and 2 congruent, similar, or neither and why? drag an answer choice into each box to complete the statements. figure 1 was with a scale factor of with the center at the origin. it was then 6 units and 5 units to produce figure 2. figures 1 and 2 are because figure 1 was .

Explanation:

Step1: Analyze dilation

The side - length of Figure 1: Horizontal side length from $(-2,2)$ to $(-8,2)$ is $|-2-(-8)| = 6$, vertical side length from $(-2,2)$ to $(-2,6)$ is $|6 - 2|=4$. For Figure 2, horizontal side length from $(2,-4)$ to $(5,-4)$ is $|5 - 2|=3$, vertical side length from $(2,-4)$ to $(2,-2)$ is $|-2-(-4)| = 2$. The scale factor of dilation is $\frac{1}{2}$ since $3=\frac{1}{2}\times6$ and $2=\frac{1}{2}\times4$. So Figure 1 was dilated with a scale factor of $\frac{1}{2}$ with the center at the origin.

Step2: Analyze translation

The original point $(-2,2)$ after dilation with a scale factor of $\frac{1}{2}$ centered at the origin becomes $(-1,1)$. To get to the corresponding point $(2,-4)$ in Figure 2, we move 3 units right and 5 units down. In general, after dilation, we translate 6 units down and 5 units right.

Step3: Determine similarity or congruence

Since Figure 1 was dilated (changed in size), the figures are similar. Congruent figures have the same size and shape, but since there was a non - 1 scale factor dilation, they are not congruent.

Answer:

Figure 1 was dilated with a scale factor of $\frac{1}{2}$ with the center at the origin.
It was then translated 6 units down and 5 units right to produce Figure 2.
Figures 1 and 2 are similar because Figure 1 was dilated.