Question

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

u( , )
v( , )
w( , )

Explanation:

Step1: Identify original coordinates

$U(-1,-2)$, $V(-1,2)$, $W(1,-2)$

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 $U$: $x=-1,y = - 2$, so $U'=(5\times(-1),5\times(-2))=(-5,-10)$
For point $V$: $x=-1,y = 2$, so $V'=(5\times(-1),5\times2)=(-5,10)$
For point $W$: $x = 1,y=-2$, so $W'=(5\times1,5\times(-2))=(5,-10)$

Answer:

$U'(-5,-10)$
$V'(-5,10)$
$W'(5,-10)$