graph the image of parallelogram defg after a dilation with a scale factor of $\frac{1}{2}$, centered at the…

Explanation:

Step1: Identify original coordinates

$D(-8, -10), E(-4, -10), G(3, 10), F(9, 10)$

Step2: Apply dilation formula

For each point $(x,y)$, new point is $\left(\frac{1}{2}x, \frac{1}{2}y\right)$

• $D': \left(\frac{1}{2}(-8), \frac{1}{2}(-10)\right) = (-4, -5)$
• $E': \left(\frac{1}{2}(-4), \frac{1}{2}(-10)\right) = (-2, -5)$
• $G': \left(\frac{1}{2}(3), \frac{1}{2}(10)\right) = (1.5, 5)$
• $F': \left(\frac{1}{2}(9), \frac{1}{2}(10)\right) = (4.5, 5)$

Step3: Plot and connect new points

Connect $D'(-4,-5)$, $E'(-2,-5)$, $F'(4.5,5)$, $G'(1.5,5)$ in order.

Answer:

The coordinates of the dilated parallelogram $D'E'F'G'$ are: $D'(-4, -5)$, $E'(-2, -5)$, $G'(1.5, 5)$, $F'(4.5, 5)$ (When graphed, these points form the dilated image centered at the origin with scale factor $\frac{1}{2}$.)