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 (3, -4), (3, -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

Let's consider the change in size. If we look at the side - lengths of the rectangles, we can find the scale factor. For example, if we consider the horizontal side - lengths. In Figure 1, if we consider the horizontal side with endpoints (-2, 2) and (-8, 2), the length is $|-2-(-8)| = 6$. In Figure 2, for the corresponding horizontal side with endpoints (2, - 4) and (3, - 4), the length is $|3 - 2|=1$. So, Figure 1 was dilated with a scale factor of $\frac{1}{6}$ with the center at the origin.

Step2: Analyze translation

After dilation, we need to find the translation. If we take a point from the dilated - Figure 1 (after dilation with scale factor $\frac{1}{6}$) and compare it to the corresponding point in Figure 2. Let's take the top - left point. After dilation, we then need to move the dilated figure. It was then translated 6 units right and 5 units down to produce Figure 2.

Step3: Determine similarity/congruence

Figures 1 and 2 are similar because Figure 1 was dilated (changed in size) and then translated. Dilation changes the size of a figure while translation just moves it, and similar figures have the same shape but not necessarily the same size.

Answer:

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