Question

graph the image of parallelogram qrst after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Identify the coordinates of the original parallelogram

From the graph, we can see that the coordinates of the parallelogram $QRST$ are $Q(-3,1)$, $R(0,1)$, $S(1,2)$, $T(-2,2)$.

Step2: Apply the dilation formula

The formula for dilation centered at the origin with a scale factor $k$ is $(x,y)\to(kx,ky)$. Here $k = 5$.
For point $Q(-3,1)$: $( - 3\times5,1\times5)=(-15,5)$
For point $R(0,1)$: $(0\times5,1\times5)=(0,5)$
For point $S(1,2)$: $(1\times5,2\times5)=(5,10)$
For point $T(-2,2)$: $(-2\times5,2\times5)=(-10,10)$

Step3: Graph the new parallelogram

Plot the points $Q'(-15,5)$, $R'(0,5)$, $S'(5,10)$, $T'(-10,10)$ and connect them to form the dilated parallelogram.

Answer:

Graph the parallelogram with vertices $Q'(-15,5)$, $R'(0,5)$, $S'(5,10)$, $T'(-10,10)$ on the given coordinate - plane.