Question

A figure is dilated using a scale factor of -1. how can you obtain the image without using a dilation? Explain your reasoning. ​

Answer 1

Answer: Rotate the point 180 degrees around the origin

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Explanation:

Consider the point (2,3). Applying a dilation of scale factor -1 means we multiply each coordinate by -1. That moves us from (2,3) to (-2,-3). This rotates the point 180 degrees about the origin. It can be done clockwise or counterclockwise.

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Extra Side Notes:

• The 180 degree rotation rule is $(x,y) \to (-x,-y)$
• The three points (x,y), (-x,-y) and (0,0) all are on the same straight line.
• The preimage and image are the same size, since the absolute value of the scale factor is 1. The rotation preserves the size.

Answer 2

Rotate it about 180 degrees