Question

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the parallelogram ghij is a dilation of the parallelogram ghij. what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Identify corresponding points

Choose corresponding vertices, e.g., $H(-5, 0)$ and $H'(-1, 0)$; $G(-9, -10)$ and $G'(-2, -2)$.

Step2: Calculate scale factor (x-coordinate ratio)

Use the ratio of the dilated point's coordinate to the original point's coordinate.
$\text{Scale factor} = \frac{H'_x}{H_x} = \frac{-1}{-5} = \frac{1}{5}$

Step3: Verify with y-coordinate ratio

Check with the y-coordinates of $G$ and $G'$:
$\text{Scale factor} = \frac{G'_y}{G_y} = \frac{-2}{-10} = \frac{1}{5}$

Answer:

$\frac{1}{5}$