Subjects geometry

Quadrilateral Dilation 1647B1

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1. The problem asks if the lighter colored quadrilateral is a dilation of the smaller quadrilateral. 2. A dilation means the shapes are similar: all corresponding angles are congruent (equal) and all corresponding sides are proportional (scaled by the same factor). 3. The smaller quadrilateral is a square from $x=-6$ to $x=-1$ and $y=3$ to $y=8$, so its side length is $|-1 - (-6)| = 5$ units. 4. The lighter quadrilateral is a square from $x=1$ to $x=7$ and $y=-7$ to $y=-1$, so its side length is $|7 - 1| = 6$ units. 5. Since both are squares, all corresponding angles are $90^\circ$, so angles are congruent. 6. Check if side lengths are proportional: ratio is $\frac{6}{5}$. 7. Since all sides of the smaller square are 5 and all sides of the larger square are 6, the side pairs are proportional by $\frac{6}{5}$. 8. Therefore, the lighter quadrilateral is a dilation of the smaller one because angles are congruent and sides are proportional. Final answer: Yes, all corresponding angles are congruent and corresponding side pairs are proportional.