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'?

Question

Coordinate A (-7,-5)
Coordinate B (-4,3)
Coordinate C (5, 6)
Coordinate D (2,-2)

Answer 1

To find the coordinates of vertex D' after dilating the parallelogram with respect to the origin using a magnitude of \( \frac{1}{2} \), we multiply each coordinate of vertex D by \( \frac{1}{2} \).

Vertex D has coordinates (2, -2).

Applying the dilation:

\[ D' = \left( \frac{1}{2} \times 2, \frac{1}{2} \times -2 \right) = (1, -1) \]

Therefore, the coordinates of vertex D' after the dilation are \( (1, -1) \).