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

The original coordinates of point $D$ are $(1,-1)$, of point $E$ are $(1,2)$, and of point $F$ are $(-2,0)$.

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 $(x',y')=(k\times x,k\times y)$. Here $k = 5$.
For point $D$: $x'=5\times1 = 5$, $y'=5\times(-1)=-5$.
For point $E$: $x'=5\times1 = 5$, $y'=5\times2 = 10$.
For point $F$: $x'=5\times(-2)=-10$, $y'=5\times0 = 0$.

Answer:

$D(5,-5)$
$E(5,10)$
$F(-10,0)$