Question

if an image of a triangle is congruent to the pre - image, what is the scale factor of the dilation?
0.1
\\( \frac { 1 } { 2 } \\)
1
10

Explanation:

Step1: Recall the property of dilation

Dilation is a transformation that changes the size of a figure. If the scale factor \(k\) of a dilation is \(k = 1\), the image is congruent to the pre - image.

Step2: Analyze other scale factors

If \(k=0.1=\frac{1}{10}\), the image is smaller than the pre - image. If \(k = \frac{1}{2}\), the image is also smaller than the pre - image. If \(k = 10\), the image is larger than the pre - image. Only when \(k = 1\), the size of the image is the same as the pre - image (by the formula for dilation: if a point \((x,y)\) is dilated with center at the origin by a scale factor \(k\), the new point is \((kx,ky)\). When \(k = 1\), \((x,y)\) maps to \((x,y)\)).

Answer:

C. 1