Question

analyzing a scale factor
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 larger than the pre - image because ( n = 1 ).
the image will be a triangle because ( n = 1 ).
the image will be smaller than the pre - image because ( n = 1 ).

Explanation:

When a figure is dilated by a scale factor \(n = 1\), each side length of the image is \(n\) times the corresponding side length of the pre - image. So, if \(n = 1\), the side lengths of the image and pre - image are equal. Congruent figures have equal corresponding side lengths. A dilation with \(n=1\) does not change the shape (a rectangle remains a rectangle, not a triangle). If \(n> 1\) the image is larger than the pre - image and if \(n<1\) the image is smaller than the pre - image.

Answer:

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