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

$S(-2,-1)$, $T(1,-1)$, $U(1,1)$, $V(-2,1)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 5$, the new coordinates $(x',y')$ of a point $(x,y)$ are given by $(x',y')=(kx,ky)$.
For point $S(-2,-1)$: $x'=5\times(-2)=-10$, $y'=5\times(-1)=-5$, so $S'(-10,-5)$
For point $T(1,-1)$: $x'=5\times1 = 5$, $y'=5\times(-1)=-5$, so $T'(5,-5)$
For point $U(1,1)$: $x'=5\times1 = 5$, $y'=5\times1 = 5$, so $U'(5,5)$
For point $V(-2,1)$: $x'=5\times(-2)=-10$, $y'=5\times1 = 5$, so $V'(-10,5)$

Answer:

$S'(-10,-5)$, $T'(5,-5)$, $U'(5,5)$, $V'(-10,5)$