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

Explanation:

Step1: Identify original coordinates

Let's assume the coordinates of the vertices of parallelogram $QRST$ are $Q(-3,1)$, $R(0,1)$, $S(1,2)$, $T(-2,2)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 5$, the formula to find the new coordinates $(x',y')$ of a point $(x,y)$ is $(x',y')=(k\times x,k\times y)$. For point $Q(-3,1)$: $Q'=(5\times(-3),5\times1)=(-15,5)$. For point $R(0,1)$: $R'=(5\times0,5\times1)=(0,5)$. For point $S(1,2)$: $S'=(5\times1,5\times2)=(5,10)$. For point $T(-2,2)$: $T'=(5\times(-2),5\times2)=(-10,10)$.

Step3: Graph the new parallelogram

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

Answer:

Graph the parallelogram with vertices $(-15,5)$, $(0,5)$, $(5,10)$, $(-10,10)$.