Question

circle x and circle y are shown. complete the steps to prove circle x is similar to circle y. enter your answers in the boxes. 1 translate circle x units to the left and units down 2 dilate circle x by a scale factor of about the origin 3 circle y can be obtained from circle x by a sequence of transformations. 4 therefore, circle x is similar to circle y

Explanation:

Step1: Find the center - point coordinates

The center of Circle X is at (6, 6) and the center of Circle Y is at (- 2, 2). To move the center of Circle X to the center of Circle Y, we need to move 8 units to the left (6 - (-2)=8) and 4 units down (6 - 2 = 4).

Step2: Find the scale - factor

Let the radius of Circle X be \(r_X\) and the radius of Circle Y be \(r_Y\). By counting the grid - squares, assume the radius of Circle X is 3 units and the radius of Circle Y is 1.5 units. The scale factor \(k=\frac{r_Y}{r_X}=\frac{1.5}{3}=\frac{1}{2}\)

Answer:

1. 8, 4
2. \(\frac{1}{2}\)
3. (No answer needed as it is a statement)
4. (No answer needed as it is a statement)