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: Analyze translation

Count the horizontal distance between corresponding points of Figure D and Figure D'. By observing the grid, we can see that to get from Figure D to Figure D', we need to translate Figure D left 4 units.

Step2: Analyze dilation

To find the scale - factor of dilation, compare the side - lengths of corresponding sides of Figure D' and Figure D''. The side - lengths of Figure D' are half of the side - lengths of Figure D''. So the scale factor of dilation is $\frac{1}{2}$. The center of dilation can be the origin $(0,0)$ (by observing the position of the figures relative to the origin).

Answer:

• First box: 4
• Second box: $\frac{1}{2}$
• Third box: 0
• Fourth box: 0