graph the image of trapezoid defg after a dilation with a scale factor of 5, centered at the origin.

Answer

Explanation:

Step1: Identify Coordinates

Find coordinates of ( D, E, F, G ):
( D(0, -2) ), ( E(1, -2) ), ( F(0, 2) ), ( G(-2, 2) ).

Step2: Apply Dilation Formula

Dilation centered at origin: ( (x, y) \to (k \cdot x, k \cdot y) ), ( k = 5 ).

( D': (5 \cdot 0, 5 \cdot -2) = (0, -10) )
( E': (5 \cdot 1, 5 \cdot -2) = (5, -10) )
( F': (5 \cdot 0, 5 \cdot 2) = (0, 10) )
( G': (5 \cdot -2, 5 \cdot 2) = (-10, 10) )

Step3: Plot New Points

Plot ( D'(0, -10) ), ( E'(5, -10) ), ( F'(0, 10) ), ( G'(-10, 10) ) and connect to form the dilated trapezoid.

Answer:

The dilated trapezoid has vertices at ( D'(0, -10) ), ( E'(5, -10) ), ( F'(0, 10) ), ( G'(-10, 10) ). (Graph by plotting these points and connecting them.)