Question

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

Explanation:

Step1: Identify original coordinates

$R(-4,4)$, $S(-2,2)$, $T(-1,-3)$, $Q(-4,-3)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, the new coordinates $(x',y')$ of a point $(x,y)$ are given by $(x',y')=(kx,ky)$. Here $k = 2$.
For point $R$: $x'=2\times(-4)=-8$, $y'=2\times4 = 8$, so new $R'(-8,8)$
For point $S$: $x'=2\times(-2)=-4$, $y'=2\times2 = 4$, so new $S'(-4,4)$
For point $T$: $x'=2\times(-1)=-2$, $y'=2\times(-3)=-6$, so new $T'(-2,-6)$
For point $Q$: $x'=2\times(-4)=-8$, $y'=2\times(-3)=-6$, so new $Q'(-8,-6)$

Answer:

$R'(-8,8)$, $S'(-4,4)$, $T'(-2,-6)$, $Q'(-8,-6)$