Question

Find the scale factor for the dilation shown.
0
4
8
12
16
20
24
28
4
8
12
16
20
24
28







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 for the dilation, you need to compare the coordinates of the original points (D, E, F, G) with their dilated counterparts (D', E', F', G').

To calculate the scale factor (k), you can use the formula:

\[
k = \frac{new \, coordinate}{original \, coordinate}
\]

For example, if a point D has coordinates (x, y) and its dilation D' has coordinates (kx, ky), you can find k for each coordinate separately and ensure they yield the same scale factor.

Let's assume that:

- The original points D, E, F, and G have coordinates:
- D (0, 0)
- E (4, 4)
- F (8, 8)
- G (12, 12)

- The dilated points D', E', F', and G' have coordinates:
- D' (0, 0)
- E' (8, 8)
- F' (16, 16)
- G' (24, 24)

Now, let's calculate the scale factor:

For point E (4, 4) to E' (8, 8):
\[
k = \frac{8}{4} = 2
\]

For point F (8, 8) to F' (16, 16):
\[
k = \frac{16}{8} = 2
\]

For point G (12, 12) to G' (24, 24):
\[
k = \frac{24}{12} = 2
\]

Since the scale factor calculated for each pair of corresponding points is the same, the scale factor of the dilation is:

\[
\text{The scale factor is } 2.
\]

You can enter **2** as your response.