Practice Test

Question 8 • Mathematics II

Which graph shows a dilation?

Answer

Image with description Coordinate plane with x- and y-axes labeled and an unlabeled square grid. A larger right triangle has a vertical left side 3 grid squares tall and a horizontal bottom side 6 grid squares long, with a slanted side connecting their endpoints. A smaller right triangle has a vertical left side 1 grid square tall and a horizontal bottom side 3 grid squares long, with a slanted side connecting their endpoints.

Image with description Coordinate plane with x- and y-axes labeled and an unlabeled square grid. A larger right triangle has a vertical left side 4 grid squares tall and a horizontal bottom side 5 grid squares long, with a slanted side connecting their endpoints. A smaller right triangle has a vertical left side 1 grid square tall and a horizontal bottom side 2 grid squares long, with a slanted side connecting their endpoints.

Image with description Coordinate plane with x- and y-axes labeled and an unlabeled square grid. A larger right triangle has a vertical left side 4 grid squares tall and a horizontal bottom side 5 grid squares long, with a slanted side connecting their endpoints. A smaller right triangle has a vertical left side 2 grid squares tall and a horizontal bottom side 3 grid squares long, with a slanted side connecting their endpoints.

Image with description Coordinate plane with x- and y-axes labeled and an unlabeled square grid. A larger right triangle has a vertical left side 3 grid squares tall and a horizontal bottom side 6 grid squares long, with a slanted side connecting their endpoints. A smaller right triangle has a vertical left side 2 grid squares tall and a horizontal bottom side 4 grid squares long, with a slanted side connecting their endpoints.

Explanation

A dilation preserves shape, so corresponding side lengths must have the same scale factor. In choice B, the larger triangle’s sides are 3 and 6 grid squares, while the smaller triangle’s corresponding sides are 2 and 4. Both ratios are 3 ÷ 2 = 6 ÷ 4 = 1.5, so the triangles are related by a dilation.

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