Question

josefina wants to prove that figures d and d are similar. what sequence of transformations could josefina perform to prove that the figures are similar? use the number pad to enter your answers in the boxes. josefina could translate figure d left units to form figure d. then she could dilate figure d by a scale factor of with a center of dilation at ( , ) to form figure d.

Explanation:

Step1: Determine translation

Count the horizontal distance between corresponding points of Figure $D$ and Figure $D'$. By observing the $x -$coordinates of corresponding vertices, we can see that to get from Figure $D$ to Figure $D'$, we move 3 units to the left.

Step2: Determine scale - factor and center of dilation

Compare the side - lengths of Figure $D'$ and Figure $D''$. The side - lengths of Figure $D''$ are twice as long as those of Figure $D'$, so the scale factor is 2. To find the center of dilation, we look for the point that stays in the same relative position. By examining the figures, we can see that the center of dilation is the point $(0,2)$.

Answer:

Josefina could translate Figure $D$ left 3 units to form Figure $D'$. Then she could dilate Figure $D'$ by a scale factor of 2 with a center of dilation at $(0,2)$ to form Figure $D''$. So the answers in order are: 3, 2, 0, 2.