Similar Figures — Quiz

Question 7 • Geometry

Which graph shows a dilation?

Answer

Image with description On a coordinate plane, the x and y axes ranges from negative 4 to positive 4 in increments of 1. 2 quadrilaterals are shown. The vertices of the larger quadrilateral are (negative 1 comma 0), (negative 3 comma 3), (1 comma 3), and (3 comma 0). The vertices of the smaller quadrilateral are (0 comma 0), (negative 1 comma 1), (1 comma 1), and (2 comma 0).

Image with description On a coordinate plane, the x and y axes range from negative 4 to positive 4 in increments of 1. 2 quadrilaterals are shown. The vertices of the larger quadrilateral are (negative 2 comma 0), (negative 4 comma 3), (0 comma 3), and (2 comma 0). The vertices of the smaller quadrilateral are (negative 1 point 5 comma 0), (negative 2 comma 2), (0 comma 2), and (0 point 5 comma 0).

Image with description On a coordinate plane, the x and y axes range from negative 5 to positive 5 in increments of 1. 2 quadrilaterals are shown. The vertices of the larger quadrilateral are (negative 2 comma 0), (negative 5 comma 3), (1 comma 3), and (4 comma 0). The vertices of the smaller quadrilateral are (negative 1 comma 0), (negative 2 comma 1), (0 comma 1), and (1 comma 0).

Image with description On a coordinate plane, the x and y axes range from negative 5 to positive 5 in increments of 1. 2 quadrilaterals are shown. The vertices of the larger quadrilateral are (negative 2 comma 0), (negative 5 comma 3), (1 comma 3), and (4 comma 0). The vertices of the smaller quadrilateral are (negative 0 point 5 comma 0), (negative 1 comma 2), (1 comma 2), and (1 point 5 comma 0).

Explanation

A dilation keeps the same scale factor for every corresponding length. In choice C, the larger quadrilateral has top and bottom widths of 6 units and a height of 3 units; the smaller has widths of 2 units and a height of 1 unit. Each corresponding length is multiplied by 1/3, so choice C shows a dilation.

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