To find the magnitude of the dilation in reference to the origin, we can compare the coordinates of a point in the original parallelogram (e.g., A) with its corresponding point in the dilated parallelogram (e.g., A').
The formula for dilation with respect to the origin can be expressed as:
\[ A' = k \cdot A \]
where \( k \) is the scale factor (dilation magnitude), and \( A \) and \( A' \) are the coordinates of the points before and after dilation, respectively.
Let's take point A and point A':
Point A: \((-2, 4)\)
Point A': \((-1, 2)\)
To find \( k \), we can use the formula for both x and y coordinates.
For the x-coordinate:
\[ -1 = k \cdot (-2) \implies k = \frac{-1}{-2} = \frac{1}{2} \]
For the y-coordinate:
\[ 2 = k \cdot 4 \implies k = \frac{2}{4} = \frac{1}{2} \]
Considering both calculations, we see that \( k \) is consistently \( \frac{1}{2} \).
Thus, the magnitude of dilation is:
\[ \frac{1}{2} \]
So the answer is:
Start Fraction 1 over 2 End Fraction
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