The Answer is 3

UpStudy Free Solution:

To determine the scale factor of the dilation that maps the solid triangle onto the dotted triangle, we compare the corresponding sides of the two triangles.

From the image:

- The length of the side of the solid triangle is \(5\).

- The corresponding side length of the dotted triangle is \(15\).

The scale factor \(k\) is the ratio of the corresponding sides:

\(k = \frac { \text { length of the side of the dotted triangle} } { \text { length of the side of the solid triangle} } = \frac { 15} { 5} = 3\)

So, the scale factor of the dilation is \(3\).

Supplemental Knowledge:

In geometry, dilation is a transformation that produces an image that is the same shape as the original figure, but is a different size. The scale factor of a dilation is the ratio of any two corresponding lengths in the pre-image and the image. If \(k\) is the scale factor, then every length in the image is \(k\) times the corresponding length in the pre-image.

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