Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.
t(

)
u(

)
v(

)
w(

)

Explanation:

Step1: Identify original coordinates

$T(-4,-4)$, $U(-4,-2)$, $V(-2,-2)$, $W(-2,-4)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 2$, the formula to find the new coordinates $(x',y')$ of a point $(x,y)$ is $(x',y')=(k\cdot x,k\cdot y)$.
For point $T$: $x=-4,y = - 4,k = 2$, so $x'=2\times(-4)=-8,y'=2\times(-4)=-8$.
For point $U$: $x=-4,y=-2,k = 2$, so $x'=2\times(-4)=-8,y'=2\times(-2)=-4$.
For point $V$: $x=-2,y=-2,k = 2$, so $x'=2\times(-2)=-4,y'=2\times(-2)=-4$.
For point $W$: $x=-2,y=-4,k = 2$, so $x'=2\times(-2)=-4,y'=2\times(-4)=-8$.

Answer:

$T'(-8,-8)$
$U'(-8,-4)$
$V'(-4,-4)$
$W'(-4,-8)$