Question

Find the scale factor for the dilation shown.
0
4
8
12
16
20
24
4
8
12
16
20
24






x
y
D'
E'
F'
D
E
F
G'
G



x y graph
Question content area bottom
Part 1
The scale factor is
  
enter your response here.

Answer 1

To find the scale factor of a dilation, we need to compare the coordinates of corresponding points before and after the dilation. In your question, it looks like you've provided a set of numbers that might represent points on a coordinate plane.

Let's assume the coordinates of points D, E, and F before dilation are (x1, y1), (x2, y2), and (x3, y3), and the coordinates of points D', E', and F' after dilation are (x'1, y'1), (x'2, y'2), and (x'3, y'3).

The formula for the scale factor \( k \) is given by:

\[
k = \frac{\text{Distance after dilation}}{\text{Distance before dilation}}
\]

Typically, we can find the scale factor by:

\[
k = \frac{x'}{x} = \frac{y'}{y}
\]

for corresponding points.

For example, if:
- D(4, 4) is dilated to D'(8, 8)
- E(8, 8) is dilated to E'(16, 16)
- F(12, 12) is dilated to F'(24, 24)

One point is enough to determine the scale factor, so using D and D':

\[
k = \frac{x'_{D}}{x_{D}} = \frac{8}{4} = 2
\]
or
\[
k = \frac{y'_{D}}{y_{D}} = \frac{8}{4} = 2
\]

Thus, the scale factor is \( 2 \).

You can repeat the same calculation with any point to verify it. Let me know if you have specific coordinates for the points involved in the dilation!