P'(-10, 15), Q'(5, -20)

UpStudy Free Solution:

To find the coordinates of the endpoints of \(\overline { P' Q' } \) after transforming \(\overline { PQ} \) by a scale factor of 2.5, we multiply the coordinates of the endpoints by the scale factor.

Given:

- \(P( - 4, 6) \)

- \(Q( 2, - 8) \)

- Scale factor = 2.5

Let's calculate the new coordinates for \(P' \) and \(Q' \).

1. Calculating \(P' \):

\(P' = ( - 4 \times 2.5, 6 \times 2.5) = ( - 10, 15) \)

2. Calculating \(Q' \):

\(Q' = ( 2 \times 2.5, - 8 \times 2.5) = ( 5, - 20) \)

So, the coordinates of the endpoints after the transformation are \(P' ( - 10, 15) \) and \(Q' ( 5, - 20) \).

Supplemental Knowledge:

When performing a dilation transformation on a line segment in a coordinate plane, each endpoint of the segment is scaled by the same factor. This means that the coordinates of each point are multiplied by the given scale factor. Dilation either enlarges or reduces the size of the figure, but the shape remains similar to the original figure.

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