Dilations — Quiz

Question 2 • Geometry

A square with a side length of 2 units is drawn on the coordinate plane with a vertex at the origin. Expand Image Which shows a dilation of the square by a scale factor of 2?

Answer

Image with description On a coordinate plane, a square has a point at negative 4 comma 0, a point at negative 4 comma 2, a point at negative 2 comma 2, and a point at negative 2 comma 0.

Image with description On a coordinate plane, a rectangle has a point at 0 comma 0, a point at 0 comma 2, a point at 4 comma 2, and a point at 4 comma 0.

Image with description On a coordinate plane, a square has a point at negative 4 comma 0, a point at negative 4 comma 4, a point at 0 comma 4, and a point at 0 comma 0.

Image with description On a coordinate plane, a square has a point at 0 comma 0, a point at 0 comma 2, a point at 2 comma 2, and a point at 2 comma 0.

Explanation

A dilation by a scale factor of 2 doubles every distance from the center of dilation, so a square with side length 2 becomes a square with side length 4. Choice C describes a square with vertices at (−4, 0), (−4, 4), (0, 4), and (0, 0), giving each side length 4. The other choices either have a different side length or are not squares.

AI-written and checked against the verified answer.

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