1 < 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'

To find the coordinates of vertex D' after dilating vertex D with respect to the origin using a magnitude of \( \frac{1}{2} \), we will use the following formula for dilation:

\[ (x', y') = \left(k \cdot x, k \cdot y\right) \]

where \( (x, y) \) are the original coordinates, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the dilation factor.

Here, the original coordinates of vertex D are \( (2, -2) \) and the dilation factor \( k \) is \( \frac{1}{2} \).

Now, apply the dilation:

\[ x' = \frac{1}{2} \cdot 2 = 1 \]

\[ y' = \frac{1}{2} \cdot (-2) = -1 \]

Thus, the new coordinates of vertex D' after the dilation would be:

\[ D' = (1, -1) \]

So, the coordinates of vertex D' are \( (1, -1) \).

what would be the coordinates of vertex B' of the parallelogram if it were dilated with respect to the origin using a magnitude of 3?

vertex B is -4, 3

To find the coordinates of vertex B' after dilating vertex B with respect to the origin using a magnitude of \( 3 \), we will again apply the dilation formula:

\[ (x', y') = \left(k \cdot x, k \cdot y\right) \]

where \( (x, y) \) are the original coordinates, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the dilation factor.

Here, the original coordinates of vertex B are \( (-4, 3) \) and the dilation factor \( k \) is \( 3 \).

Now, apply the dilation:

1. For the \( x \)-coordinate: \[ x' = 3 \cdot (-4) = -12 \]

2. For the \( y \)-coordinate: \[ y' = 3 \cdot 3 = 9 \]

Thus, the new coordinates of vertex B' after the dilation would be:

\[ B' = (-12, 9) \]

So, the coordinates of vertex B' are \( (-12, 9) \).