If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?
A. 0.1
B. $\frac{1}{2}$
C. 1
D. 10
Answer (1)
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 is 1 .
Explanation
Understanding Dilation and Congruence When a figure is dilated, its size changes according to a scale factor. If the image of a triangle is congruent to its pre-image, it means the size and shape of the triangle remain unchanged after the dilation.
Determining the Scale Factor Since the image and pre-image are congruent, the scale factor must be 1, as multiplying the side lengths of the original triangle by 1 results in the same side lengths, thus preserving congruence.
Conclusion Therefore, the scale factor of the dilation is 1.
Examples
Imagine you have a photograph that you want to enlarge or reduce. If you print the photograph at the exact same size as the original, you are essentially performing a dilation with a scale factor of 1. The copy is congruent to the original, meaning it has the same size and shape. This concept is useful in various applications, such as mapmaking, where maintaining accurate proportions is crucial.
