Question

graph the image of parallelogram bcde after a dilation with a scale factor of 3, 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 $(x',y')=(k\cdot x,k\cdot y)$. Here $k = 3$.

Step2: Identify the coordinates of the vertices of parallelogram $BCDE$

Let's assume the coordinates of the vertices: $B(-3,-3)$, $C(-2,-1)$, $D(1,3)$, $E(2,1)$.

Step3: Apply the dilation formula to each vertex

For point $B(-3,-3)$:
$B'=(3\times(-3),3\times(-3))=(-9,-9)$
For point $C(-2,-1)$:
$C'=(3\times(-2),3\times(-1))=(-6,-3)$
For point $D(1,3)$:
$D'=(3\times1,3\times3)=(3,9)$
For point $E(2,1)$:
$E'=(3\times2,3\times1)=(6,3)$

Step4: Graph the new parallelogram

Plot the points $B'(-9,-9)$, $C'(-6,-3)$, $D'(3,9)$, $E'(6,3)$ on the coordinate - plane and connect them to form the dilated parallelogram.

Answer:

Graph the parallelogram with vertices $B'(-9,-9)$, $C'(-6,-3)$, $D'(3,9)$, $E'(6,3)$ on the given coordinate grid.