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

Let the coordinates of point $U$ be $(- 1,-2)$, point $V$ be $(-1,2)$ and point $W$ be $(1,-2)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, the formula to find the new coordinates $(x',y')$ of a point $(x,y)$ is $(x',y')=(k\cdot x,k\cdot y)$. Here $k = 5$.
For point $U(-1,-2)$:
$x'=5\times(-1)=-5$, $y'=5\times(-2)=-10$. So the new coordinates of $U$ are $(-5,-10)$.
For point $V(-1,2)$:
$x'=5\times(-1)=-5$, $y'=5\times2 = 10$. So the new coordinates of $V$ are $(-5,10)$.
For point $W(1,-2)$:
$x'=5\times1 = 5$, $y'=5\times(-2)=-10$. So the new coordinates of $W$ are $(5,-10)$.

Answer:

The coordinates of $U$ after dilation are $(-5,-10)$, the coordinates of $V$ after dilation are $(-5,10)$, and the coordinates of $W$ after dilation are $(5,-10)$.