Question

analyzing a description of a transformation
all side lengths of \\( \triangle j k l \\) equal 2 units. a transformation maps \\( \triangle j k l \\) to \\( \triangle j k l \\). the length of side \\( \overline{j k} \\) is 5 units. is this
a rigid transformation?
no, there is no one - to - one mapping of all the points of the pre - image to the image.
no, at least one segment length is not preserved, making this a nonrigid transformation.
yes, the vertices of the pre - image map to the vertices of the image.
yes, all of the side lengths of the pre - image are proportionate to the image.

Explanation:

A rigid transformation preserves the side lengths and angle measures of a figure. In the pre - image $\triangle JKL$, all side lengths are 2 units. The transformation maps $\triangle JKL$ to $\triangle J'K'L'$, and the length of $\overline{J'K'}$ is 5 units. This means at least one segment length (the side corresponding to $\overline{J'K'}$ from the pre - image side of length 2) is not preserved. For a transformation to be rigid, all segment lengths must be preserved. So this is a non - rigid transformation.

Answer:

No, at least one segment length is not preserved, making this a nonrigid transformation.