Question

write the coordinates of the vertices after a dilation with a scale factor of 5, centered at the origin.
a(□,□)
b(□,□)
c(□,□)
d(□,□)

Explanation:

Step1: Identify original coordinates

$A(-1,-2)$, $B(-1,0)$, $C(2,0)$, $D(2, - 1)$

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 $A$: $x=-1,y = - 2$, so $A'=(5\times(-1),5\times(-2))=(-5,-10)$
For point $B$: $x=-1,y = 0$, so $B'=(5\times(-1),5\times0)=(-5,0)$
For point $C$: $x = 2,y = 0$, so $C'=(5\times2,5\times0)=(10,0)$
For point $D$: $x = 2,y=-1$, so $D'=(5\times2,5\times(-1))=(10,-5)$

Answer:

$A'(-5,-10)$
$B'(-5,0)$
$C'(10,0)$
$D'(10,-5)$