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 rotated figure 1 about the origin 180° followed by a dilation and a translation. he rotated figure 1 clockwise 90° followed by a translation. 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.

Explanation:

Step1: Analyze rotation about origin 180°

A 180 - degree rotation about the origin changes $(x,y)$ to $(-x,-y)$. For Figure 1 with vertices $(-2,2),(-2,6),(-8,6),(-8,2)$, after 180 - degree rotation about the origin, the vertices become $(2, - 2),(2,-6),(8,-6),(8,-2)$. Then dilation and translation would not map it to Figure 2.

Step2: Analyze 90 - degree clockwise rotation

A 90 - degree clockwise rotation about the origin changes $(x,y)$ to $(y,-x)$. For vertices of Figure 1: $(-2,2)$ becomes $(2,2)$, $(-2,6)$ becomes $(6,2)$, $(-8,6)$ becomes $(6,8)$, $(-8,2)$ becomes $(2,8)$. After a translation, it can be mapped to Figure 2.

Step3: Analyze reflection in y - axis

Reflection in the $y$ - axis changes $(x,y)$ to $(-x,y)$. Starting with Figure 1 vertices, after reflection in $y$ - axis and then translation and rotation, it cannot be mapped to Figure 2.

Step4: Analyze double - reflection

Reflection in the $x$ - axis changes $(x,y)$ to $(x,-y)$ and then reflection in the $y$ - axis changes $(x,-y)$ to $(-x,-y)$. This will not map Figure 1 to Figure 2.

Answer:

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