Question

graph the image of △qrs after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

Let's assume the coordinates of the vertices of $\triangle QRS$ are $Q(x_1,y_1)$, $R(x_2,y_2)$, $S(x_3,y_3)$. From the graph, if $Q(- 2,1)$, $R(2,1)$, $S(-2,2)$.

Step2: Apply dilation formula

The formula for dilation centered at the origin with scale - factor $k$ is $(x,y)\to(kx,ky)$. Here $k = 4$.
For point $Q(-2,1)$: $(x,y)\to(4\times(-2),4\times1)=(-8,4)$.
For point $R(2,1)$: $(x,y)\to(4\times2,4\times1)=(8,4)$.
For point $S(-2,2)$: $(x,y)\to(4\times(-2),4\times2)=(-8,8)$.

Step3: Graph the new triangle

Plot the points $Q'(-8,4)$, $R'(8,4)$ and $S'(-8,8)$ on the coordinate - plane and connect them to form $\triangle Q'R'S'$.

Answer:

Plot the points $(-8,4)$, $(8,4)$ and $(-8,8)$ and connect them to get the dilated triangle.