To determine the magnitude of dilation from parallelogram ABCD to its dilated image A'B'C'D', you need to know the coordinates of the vertices of both the original and the dilated figure. The magnitude of dilation can be calculated using the formula:
\[ \text{Magnitude of Dilation} = \frac{\text{Distance from the origin to a point on A'B'C'D'}}{\text{Distance from the origin to the corresponding point on ABCD}} \]
Without specific coordinates, we can derive the dilation factor by comparing the distances of corresponding points from the origin.
For example, if point A is at (x, y) and point A' is at (kx, ky), then the magnitude of dilation (k) can be computed as:
\[ k = \frac{\sqrt{(kx)^2 + (ky)^2}}{\sqrt{x^2 + y^2}} \]
If you're given certain values in your question's image or a numeric representation of the vertices, plug those coordinates into the formula to find the correct option.
From the choices provided, the possible dilation factors are 2, \( \frac{1}{2} \), \( \frac{1}{3} \), and 1. You should choose the one that fits the computed ratio based on the distances from the origin.
Since there's no image or specific coordinates available in your message, I can't provide a direct answer. Please calculate using the distances as per the formula outlined above. If you have the coordinates, I'd be happy to help you further!
3 answers