Question

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

Explanation:

A rigid transformation (like translation, rotation, reflection) preserves the side lengths and angles of a figure. In $\triangle JKL$, all sides are 2 units. After transformation, $\overline{J'K'}$ is 5 units, so a side length changed. Non - rigid transformations (like dilation) change side lengths. So the transformation isn't rigid because a segment length isn't preserved.

Answer:

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