Question

Suppose the parallelogram on the coordinate plane was dilated with respect to the origin using a magnitude of 1/2. What would be the coordinates of vertex D′?

Answer 1

To determine the coordinates of vertex \( D' \) after dilating a vertex \( D \) of a parallelogram with respect to the origin by a scale factor of \( \frac{1}{2} \), you will need the original coordinates of vertex \( D \).

The formula for dilation of a point \( (x, y) \) with respect to the origin by a scale factor \( k \) is given by:

\[
(x', y') = (kx, ky)
\]

In this case, using a scale factor of \( \frac{1}{2} \):

\[
(x', y') = \left(\frac{1}{2}x, \frac{1}{2}y\right)
\]

If you provide the specific coordinates of vertex \( D \), I can calculate the coordinates of vertex \( D' \) for you.