If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?
A. 0.1
B. [tex]$\frac{1}{2}$[/tex]
C. 1
D. 10
Answer (2)
Dilation changes the size of a figure by a scale factor.
Congruent figures have the same size and shape.
If the image is congruent to the pre-image, the size remains unchanged.
The scale factor of the dilation is 1 .
Explanation
Understanding Congruence and Dilation When a figure is dilated, its size changes according to the scale factor. If the image of a triangle is congruent to its pre-image, it means the size and shape of the triangle remain the same after the dilation.
Determining the Scale Factor Since the image is congruent to the pre-image, the scale factor must be 1. Multiplying the side lengths of the original triangle by a scale factor of 1 results in the same side lengths in the image, thus preserving the size and shape.
Conclusion Therefore, the scale factor of the dilation is 1.
Examples
Imagine you have a photograph and you want to create a copy that is exactly the same size as the original. If you use a photocopier to make a congruent copy, the scale factor is 1, meaning the copy is neither enlarged nor reduced. This ensures that all dimensions of the copy match the original photograph perfectly, preserving all details.
The scale factor of the dilation when an image is congruent to the pre-image is 1, indicating that the sizes remain unchanged. Therefore, the correct answer is C. 1.
;
