Question

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

Explanation:

Step1: Identify the coordinates of the original square

The coordinates of square $DEFG$ are $D(-6,-4)$, $E(4,-4)$, $F(4,5)$, $G(-6,5)$.

Step2: Apply the dilation formula

For a dilation centered at the origin with scale - factor $k = 2$, the formula to find the new coordinates $(x',y')$ of a point $(x,y)$ is $(x',y')=(k\cdot x,k\cdot y)$.
For point $D(-6,-4)$: $D'=(2\times(-6),2\times(-4))=(-12,-8)$.
For point $E(4,-4)$: $E'=(2\times4,2\times(-4))=(8,-8)$.
For point $F(4,5)$: $F'=(2\times4,2\times5)=(8,10)$.
For point $G(-6,5)$: $G'=(2\times(-6),2\times5)=(-12,10)$.

Step3: Graph the new square

Plot the points $D'(-12,-8)$, $E'(8,-8)$, $F'(8,10)$, $G'(-12,10)$ on the coordinate - plane and connect them to form the dilated square.

Answer:

The new square has vertices $D'(-12,-8)$, $E'(8,-8)$, $F'(8,10)$, $G'(-12,10)$ which should be graphed on the given coordinate grid.