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 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:

Step1: Recall the effect of dilation scale factor

When a figure is dilated with a scale factor \(n\), if \(n>1\), the image is larger than the pre - image; if \(0 < n<1\), the image is smaller than the pre - image; if \(n = 1\), the dilation transformation does not change the size of the figure.

Step2: Analyze each option

• Option A: When \(n = 1\), the image is not smaller. Since \(n=1

eq0 < n<1\).

• Option B: For a dilation with \(n = 1\), every side length of the rectangle (pre - image) is multiplied by \(1\). So, the image has the same side lengths as the pre - image, and congruent figures have the same shape and size.
• Option C: When \(n = 1\), the image is not larger. Since \(n = 1

eq n>1\).

• Option D: Dilation of a rectangle with any non - zero scale factor \(n\) (here \(n = 1\)) will still result in a rectangle (same shape), not a triangle.

Answer:

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