Question

Polygon LMNPQR is shown on the coordinate grid and models the shape of the garden in a park. Polygon LMNPQR will be dialed with the origin as the center of the dilation to create polygon LMmPQR the vertex Qwill be located at (21,7).

Answer 1

The question involves a geometry concept where a polygon on a coordinate grid is being dilated with the origin as the center of dilation, and the new position of vertex Q will be at (21,7). The problem requires finding a scale factor and applying it to determine the new vertices' positions.

Step-by-step explanation:

The student's question involves the concept of dilation in geometry, which is a transformation that produces an image that is the same shape as the original, but is a different size. In this case, the student is asked about the dilation of a polygon on a coordinate grid.

The center of the dilation is the origin, and the new location of vertex Q will be at (21,7). This transformation involves using a scale factor to determine the new positions of the other vertices of the polygon LMNPQR to create the image polygon L'M'N'P'Q'R'.

To solve this problem, the scale factor needed for dilation can be determined by comparing the original coordinates of vertex Q to the new coordinates (21,7).

Once the scale factor is found, it can be applied to all the vertices of the polygon to find their new positions, ensuring that the shape's proportions remain consistent, but the size changes according to the scale factor.