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

$U(-4, - 2)$, $V(-2,-2)$, $W(-2,-4)$, $T(-4,-4)$

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 $U$: $(-4\times2,-2\times2)=(-8,-4)$
For point $V$: $(-2\times2,-2\times2)=(-4,-4)$
For point $W$: $(-2\times2,-4\times2)=(-4,-8)$
For point $T$: $(-4\times2,-4\times2)=(-8,-8)$

Answer:

$U'(-8,-4)$, $V'(-4,-4)$, $W'(-4,-8)$, $T'(-8,-8)$