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

From the graph, $D(5, - 2)$, $E(5,2)$, $F(-4,3)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, the formula is $(x,y)\to(kx,ky)$. Here $k = 2$.
For point $D$: $x = 5,y=-2$, so $D'(2\times5,2\times(-2))=(10,-4)$.
For point $E$: $x = 5,y = 2$, so $E'(2\times5,2\times2)=(10,4)$.
For point $F$: $x=-4,y = 3$, so $F'(2\times(-4),2\times3)=(-8,6)$.

Answer:

$D'(10,-4)$
$E'(10,4)$
$F'(-8,6)$