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 smaller than the pre - image because ( n = 1 ).
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 ).

Explanation:

When a figure is dilated by a scale factor \(n\), if \(n = 1\), the dilation formula \( (x,y)\to(nx,ny)\) gives \((x,y)\to(1\times x,1\times y)=(x,y)\). Congruent figures have the same shape and size. Since the scale factor \(n = 1\) does not change the dimensions of the rectangle (the pre - image), the image after dilation has the same shape (still a rectangle) and size as the pre - image.

Answer:

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