Question

graph the image of square defg after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify original square vertices

From the graph:
$D(-5, -5)$, $E(5, -5)$, $F(5, 5)$, $G(-5, 5)$

Step2: Apply dilation rule

For dilation centered at origin with scale factor $k=2$, multiply each coordinate by 2:
New $D'$: $(-5 \times 2, -5 \times 2) = (-10, -10)$
New $E'$: $(5 \times 2, -5 \times 2) = (10, -10)$
New $F'$: $(5 \times 2, 5 \times 2) = (10, 10)$
New $G'$: $(-5 \times 2, 5 \times 2) = (-10, 10)$

Step3: Plot and connect vertices

Plot $D'(-10,-10)$, $E'(10,-10)$, $F'(10,10)$, $G'(-10,10)$, then connect the points in order to form the dilated square.

Answer:

The vertices of the dilated square are $D'(-10, -10)$, $E'(10, -10)$, $F'(10, 10)$, $G'(-10, 10)$. When plotted and connected, these form a square centered at the origin with side length 20, twice the size of the original square.