Bot GPT 4-o mini To determine the magnitude of the dilation from parallelogram ABCD to parallelogram A'B'C'D', we need to find the scale factor of the dilation. The scale factor can be calculated by comparing the coordinates of corresponding points before and after dilation.
We can select any point, but let's use point A for this example.
Coordinates of point A:
- A = (-2, 4)
- A' = (-1, 2)
To find the scale factor (k), we can use the formula:
\[ k = \frac{\text{distance from the origin to A'}}{\text{distance from the origin to A}} \]
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Calculate the distance from the origin to A: \[ \text{Distance to A} = \sqrt{(-2)^2 + (4)^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5} \]
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Calculate the distance from the origin to A': \[ \text{Distance to A'} = \sqrt{(-1)^2 + (2)^2} = \sqrt{1 + 4} = \sqrt{5} \]
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Now, calculate the scale factor: \[ k = \frac{\text{Distance to A'}}{\text{Distance to A}} = \frac{\sqrt{5}}{2\sqrt{5}} = \frac{1}{2} \]
Thus, the magnitude of the dilation is \(\frac{1}{2}\).
The correct answer is: b. 1/2
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