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.

Answer 1

Answer:

The answer to this question is B

Answer 2

Answer:  The true statement is (B) The image will be congruent to the pre-image because n = 1.

Step-by-step explanation: Given that a rectangle is dilated by a scale factor of n = 1. We are to select the true statement from the given options.

We have for two similar figures, one dilated (smaller or larger) from the other,

the scale factor is the ratio of the length of a side of dilated figure to the length of the corresponding side of the original figure.

Let ABCD be the original rectangle and A'B'C'D' be the dilated rectangle, then we have by the definition of the scale factor that

$\dfrac{A'B'}{AB}=\dfrac{B'C'}{BC}=\dfrac{C'D'}{CD}=\dfrac{D'A'}{DA}=n=1,\\\\\\\Rightarrow A'B'=AB,~B'C'=BC,~C'D'=CD,~D'A'=DA.$

Since the lengths of all the sides of rectangle ABCD are equal to the lengths of the corresponding sides of the dilated rectangle A'B'C'D', therefore both the figures are congruent.

Thus, (B) is the correct option.