Question

in the diagram below, figure klmn is the image of figure kopq after it has been rotated. determine if each pair of sides are corresponding sides. select yes or no for each pair of sides. op and lm yes no ko and kl yes no mn and op yes no kl and kq yes no

Explanation:

Step1: Understand the concept of rotation

Rotation is a transformation that turns a figure around a fixed point. When a figure is rotated, each point of the original figure (pre - image) has a corresponding point in the rotated figure (image). Corresponding sides are the sides that match up between the pre - image and the image.

Step2: Analyze each pair of sides

• For \(\overline{KL}\) and \(\overline{KO}\):

Since \(KLMN\) is the image of \(KOPQ\) after rotation, and in a rotation, the order of the vertices changes. The side \(\overline{KL}\) in the image \(KLMN\) corresponds to the side \(\overline{KO}\) in the pre - image \(KOPQ\) (because of the rotational transformation around point \(K\)).

• For \(\overline{KO}\) and \(\overline{KL}\):

This is the reverse of the correct correspondence. \(\overline{KO}\) is in the pre - image and \(\overline{KL}\) is in the image. The correct correspondence is \(\overline{KL}\to\overline{KO}\) (image to pre - image), not \(\overline{KO}\to\overline{KL}\) in terms of correspondence (pre - image to image is wrong here).

• For \(\overline{MN}\) and \(\overline{OP}\):

In a rotation, the order of the vertices is important. If we consider the rotation of the polygon \(KOPQ\) to get \(KLMN\), the side \(\overline{MN}\) does not correspond to \(\overline{OP}\). The side \(\overline{PQ}\) (in \(KOPQ\)) would correspond to a side in \(KLMN\) based on the rotational movement of vertices.

• For \(\overline{OP}\) and \(\overline{LM}\):

The side \(\overline{OP}\) in \(KOPQ\) does not correspond to \(\overline{LM}\) in \(KLMN\). The side \(\overline{PQ}\) (in \(KOPQ\)) and a side in \(KLMN\) (say \(\overline{MN}\) depending on the rotation direction and angle) would have a different relationship.

Answer:

\(\overline{KL}\) and \(\overline{KO}\): Yes; \(\overline{KO}\) and \(\overline{KL}\): No; \(\overline{MN}\) and \(\overline{OP}\): No; \(\overline{OP}\) and \(\overline{LM}\): No