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

3
3

2
2

1
1

12

Answer 1

To determine the magnitude of the dilation from polygon ABCD to polygon A′B′C′D′, you would typically find the distance from the origin to a point on polygon ABCD and compare it to the distance from the origin to the corresponding point on polygon A′B′C′D′.

If the dilation factor is known, it often can be expressed as the ratio of a distance from the origin to the corresponding vertices of the two polygons.

If the distances from the origin to a vertex \( (x, y) \) of polygon ABCD and the corresponding vertex \( (x', y') \) of polygon A′B′C′D′ are R₁ and R₂ respectively, the magnitude of the dilation \( k \) can be calculated as:

\[ k = \frac{R₂}{R₁} \]

In the responses you've provided, you would have to check typical ratios based on the coordinate points. Without specific coordinates or a visual, one option among those provided must either be verified via computation or through visually estimating if the image is available.

Please check the respective distances and select the appropriate multiplicative dilation factor. If there were specific coordinates or distances mentioned in the problem, those would guide you to the answer. If you would like to analyze those proportions, please provide more details!