Question

The blue figure is a dilation image of the black figure. The origin is the center of dilation. Tell whether the dilation is an enlargement or a reduction. Then find the scale factor of the dilation.
8
0
16
8
0
16
x
y



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Question content area bottom
Part 1
Is the dilation an enlargement or a​ reduction?
Enlargement
Reduction
Your answer is correct.
Part 2
The scale factor of the dilation is
  
enter your response here. ​(Simplify your​ answer.)

Answer 1

To determine whether the dilation is an enlargement or a reduction, we need to compare the coordinates of the original figure (black figure) with those of the dilated image (blue figure) after dilation.

1. **Determine Enlargement or Reduction**:
- If the coordinates of the dilated (blue) figure are farther from the origin compared to the original (black) figure, it's an enlargement.
- If the coordinates of the dilated figure are closer to the origin, it's a reduction.

Based on your statement, "the dilation is an enlargement," it can be concluded that the coordinates of the blue figure are farther away from the origin than those of the black figure.

2. **Finding the Scale Factor**:
To find the scale factor (k), you can use the formula:

\[
k = \frac{\text{dilated coordinate}}{\text{original coordinate}}
\]

If you provide the coordinates of both figures, I can assist you in calculating the specific scale factor. However, in this case, if you mentioned coordinates like \( (8, 0) \) for the original and \( (16, 0) \) for the dilated image, we can compute the scale factor as follows:

\[
k = \frac{16}{8} = 2
\]

So the scale factor is \( 2 \) (indicating an enlargement factor of 2).

If you have different numerical values, please provide them so I could give you the exact scale factor after simplification.