Questions: Graph the image of parallelogram DEFG after a dilation with a scale factor of 1/2 centered at the origin.

Transcript text: Graph the image of parallelogram DEFG after a dilation with a scale factor of $\frac{1}{2}$ centered at the origin.

Solution

Solution Steps

Step 1: Identify the coordinates of the vertices of parallelogram DEFG.

The coordinates are D(-4,-10), E(-4, -10), F(10,10), and G(4,10).

Step 2: Apply the dilation with a scale factor of 1/2.

Multiply each coordinate by 1/2:

D'(-2, -5) E'(-2, -5) F'(5, 5) G'(2, 5)

Step 3: Plot the new coordinates and connect the vertices to form the image parallelogram D'E'F'G'.

The image parallelogram D'E'F'G' will have vertices at D'(-2, -5), E'(-2, -5), F'(5, 5), and G'(2, 5). Note that since D and E have the same coordinates, so do D' and E'.

Final Answer

The image parallelogram D'E'F'G' has vertices at D'(-2, -5), E'(-2,-5), F'(5, 5), and G'(2, 5). It is half the size of the original parallelogram DEFG, centered at the origin.

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