Use the image to answer the question.

Question

Smaller polygon upper A upper B upper C upper D is graphed within larger polygon upper A prime upper B prime upper C prime upper D prime 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

1
1

3
3

2
2

12

Answer 1

To determine the magnitude of the dilation from polygon ABCD to polygon A′B′C′D′, we need to compare the coordinates of corresponding points from both polygons.

If you have the coordinates of the vertices of both polygons, you would follow these steps:

1. Calculate the distance from the origin to each vertex of polygon ABCD.
2. Calculate the distance from the origin to each corresponding vertex of polygon A′B′C′D′.
3. Divide the distance from the origin to the vertices of A′B′C′D′ by the distance from the origin to the vertices of ABCD.

The ratio found will give you the magnitude of the dilation. For instance, if:

• The distance from the origin to a vertex of ABCD is 2 units.
• The distance from the origin to the corresponding vertex of A′B′C′D′ is 6 units.

The magnitude of dilation would be 6/2 = 3.

Since you did not provide the actual coordinates of the polygons, I cannot calculate the specific magnitude of dilation. However, you can find it by using the method outlined above.

Based on the provided response choices (1, 2, 3, and 12), you would select the appropriate answer based on your calculations. If the dilation indicates a ratio of 3, then the answer would be 3.