Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Find original coordinates

From the graph, $Q(-5, - 1)$, $R(3,-1)$, $S(3,5)$, $T(-5,5)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 2$, the formula is $(x,y)\to(kx,ky)$.
For point $Q$: $x=-5,y = - 1,k = 2$, so $Q'=(2\times(-5),2\times(-1))=(-10,-2)$.
For point $R$: $x = 3,y=-1,k = 2$, so $R'=(2\times3,2\times(-1))=(6,-2)$.
For point $S$: $x = 3,y = 5,k = 2$, so $S'=(2\times3,2\times5)=(6,10)$.
For point $T$: $x=-5,y = 5,k = 2$, so $T'=(2\times(-5),2\times5)=(-10,10)$.

Answer:

$Q'(-10,-2)$
$R'(6,-2)$
$S'(6,10)$
$T'(-10,10)$