Question

a rectangle is dilated by a scale factor of ( n = 1 ). which statement is true regarding the image of the dilation?

• the image will be congruent to the pre - image because ( n = 1 ).
• the image will be smaller than the pre - image because ( n = 1 ).
• the image will be a triangle because ( n = 1 ).
• the image will be larger than the pre - image because ( n = 1 ).

Explanation:

Step1: Recall Dilation with Scale Factor 1

A dilation with a scale factor \( n = 1 \) means the transformation does not change the size of the figure. Congruent figures have the same size and shape.

Step2: Analyze Each Option

• "The image will be smaller than the pre - image because \( n = 1 \)": Incorrect, since \( n = 1 \) does not reduce size.
• "The image will be larger than the pre - image because \( n = 1 \)": Incorrect, since \( n = 1 \) does not increase size.
• "The image will be a triangle because \( n = 1 \)": Incorrect, the pre - image is a rectangle, dilation preserves the shape (it will still be a rectangle).
• "The image will be congruent to the pre - image because \( n = 1 \)": Correct, as a scale factor of 1 means the image has the same size and shape as the pre - image, so they are congruent.

Answer:

The image will be congruent to the pre - image because \( n = 1 \)