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 b curtis says there is another sequence of transformations that maps figure 1 onto figure 2. which transformations did curtis perform? he reflected figure 1 in the y - axis followed by a translation and a rotation he reflected figure 1 in the x - axis followed by a reflection in the y - axis. he rotated figure 1 about the origin 180° followed by a dilation and a translation. he rotated figure 1 clockwise 90° followed by a translation.

Explanation:

Step1: Analyze each option

• Option 1: Reflecting in the y - axis changes the sign of the x - coordinate. Then translation and rotation would further modify the figure. But this sequence does not map Figure 1 to Figure 2.
• Option 2: Reflecting in the x - axis changes the sign of the y - coordinate and then reflecting in the y - axis changes the sign of the x - coordinate. This sequence does not map Figure 1 to Figure 2.
• Option 3: Rotating 180° about the origin changes the signs of both x and y coordinates. Then dilation and translation. This sequence does not map Figure 1 to Figure 2.
• Option 4: Rotating Figure 1 clockwise 90° about the origin:

The rule for a 90 - degree clockwise rotation about the origin is \((x,y)\to(y, - x)\).
For vertex \((-2,2)\) of Figure 1, after 90 - degree clockwise rotation, it becomes \((2,2)\). Then a translation can map it to the corresponding vertex of Figure 2. For example, if we translate the rotated figure 3 units right and 6 units down, \((2,2)\) becomes \((2 + 3,2-6)=(5,-4)\) which is a vertex of Figure 2.

Answer:

He rotated Figure 1 clockwise 90° followed by a translation.