Question

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

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale factor $k$, if a point $(x,y)$ is dilated, the new - point $(x',y')$ is given by $(x',y')=(kx,ky)$. Here $k = 2$.

Step2: Identify the coordinates of the vertices of square DEFG

From the graph, the coordinates of the vertices are $D(-6,-5)$, $E(6,-5)$, $F(6,5)$, $G(-6,5)$.

Step3: Apply the dilation formula to each vertex

For point $D(-6,-5)$:
$D'=(2\times(-6),2\times(-5))=(-12,-10)$
For point $E(6,-5)$:
$E'=(2\times6,2\times(-5))=(12,-10)$
For point $F(6,5)$:
$F'=(2\times6,2\times5)=(12,10)$
For point $G(-6,5)$:
$G'=(2\times(-6),2\times5)=(-12,10)$

Step4: Graph the new square

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

Answer:

Graph the square with vertices $(-12,-10)$, $(12,-10)$, $(12,10)$, $(-12,10)$ on the given coordinate grid.