Question

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

Explanation:

Step1: Identify the coordinates of vertices

Let's assume the coordinates of the vertices of $\triangle STU$ are $S(-6,5)$, $T(6,5)$, $U(-4,1)$.

Step2: Apply the dilation rule

The rule for dilation centered at the origin with a scale - factor $k$ is $(x,y)\to(kx,ky)$. Here $k = 2$.
For point $S(-6,5)$: $( - 6\times2,5\times2)=(-12,10)$.
For point $T(6,5)$: $(6\times2,5\times2)=(12,10)$.
For point $U(-4,1)$: $(-4\times2,1\times2)=(-8,2)$.

Step3: Graph the new triangle

Plot the points $S'(-12,10)$, $T'(12,10)$ and $U'(-8,2)$ on the coordinate - plane and connect them to form the dilated triangle $\triangle S'T'U'$.

Answer:

Plot the points $(-12,10)$, $(12,10)$ and $(-8,2)$ and connect them to get the image of $\triangle STU$ after dilation.