Question

polygon y is a scaled copy of polygon x using a scale factor of \frac{1}{3}. polygon ys area is what fraction of polygon xs area?

Explanation:

Step1: Recall the area - scale factor relationship

If the scale factor of two similar polygons is \(k\), the ratio of their areas is \(k^{2}\). Here, the scale factor \(k=\frac{1}{3}\).

Step2: Calculate the ratio of the areas

We use the formula \(A_{Y}/A_{X}=k^{2}\). Substitute \(k = \frac{1}{3}\) into the formula: \(A_{Y}/A_{X}=(\frac{1}{3})^{2}\).

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Answer:

\(\frac{1}{9}\)