Question

write the coordinates of the vertices after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Identify original coordinates

$R(-2,-2)$, $S(-2,0)$, $T(0,2)$, $U(0, - 2)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, the formula is $(x,y)\to(kx,ky)$. Here $k = 5$.
For point $R$: $x=-2,y = - 2$, new coordinates are $(5\times(-2),5\times(-2))=(-10,-10)$
For point $S$: $x=-2,y = 0$, new coordinates are $(5\times(-2),5\times0)=(-10,0)$
For point $T$: $x = 0,y = 2$, new coordinates are $(5\times0,5\times2)=(0,10)$
For point $U$: $x = 0,y=-2$, new coordinates are $(5\times0,5\times(-2))=(0,-10)$

Answer:

$R'(-10,-10)$, $S'(-10,0)$, $T'(0,10)$, $U'(0,-10)$