Suppose the parallelogram A(-7,-5)B(-4,3)C(5,6)D(2,-2) on the coordinate plane was dilated with respect to the origin using a magnitude of 1/2. what would be the coordinates of vortex D'?

Answer 1

To find the coordinates of point D' after dilating point D(2, -2) with respect to the origin using a scale factor of \(\frac{1}{2}\), you can use the following formula for dilation:

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

where \(k\) is the scale factor, and \((x, y)\) are the original coordinates of point D.

For point D(2, -2):

• \(x = 2\)
• \(y = -2\)
• \(k = \frac{1}{2}\)

Now, apply the dilation:

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

Calculating each component:

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

Thus, the coordinates of point \(D'\) after dilation are \((1, -1)\).