Question

Use the image to answer the question.

Smaller polygon upper A (-1,-1), upper B (-1,1), upper C (2,3), upper D (2,-1) is graphed within larger polygon upper A prime (-2,-2), upper B prime (-2,2), upper C prime (4,6), upper D prime (4,-2), on a coordinate plane.

In the image, polygon ABCD
is dilated to form polygon A′B′C′D′
with respect to the origin. What is the magnitude of dilation?

(1 point)
Responses

2
2

3
3

1
1

12

Answer 1

To find the magnitude of dilation from polygon ABCD to polygon A'B'C'D', we can compare the coordinates of corresponding points in the two polygons.

For each vertex:

- A (-1, -1) dilates to A' (-2, -2)
- B (-1, 1) dilates to B' (-2, 2)
- C (2, 3) dilates to C' (4, 6)
- D (2, -1) dilates to D' (4, -2)

To find the dilation factor, we can use the formula for dilation (d) based on corresponding coordinates:

For point A to A':
- The x-coordinates:
\[
d = \frac{x'}{x} = \frac{-2}{-1} = 2
\]

For point B to B':
- The y-coordinates:
\[
d = \frac{y'}{y} = \frac{2}{1} = 2
\]

For point C to C':
- The x-coordinates:
\[
d = \frac{x'}{x} = \frac{4}{2} = 2
\]

For point D to D':
- The x-coordinates:
\[
d = \frac{x'}{x} = \frac{4}{2} = 2
\]

In all cases, the dilation factor (magnitude of dilation) is consistently 2.

Therefore, the answer is:

2