Question

dilate △abc with a scale factor of 8. enter the new coordinates. a = (?, ) b = (, ) c = (, ) a(0,2) b(3,-2) c(-1,-4)

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated with a scale factor $k$ centered at the origin, the new - point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Find new coordinates of point A

Given $A=(0,2)$ and $k = 8$.
$x'_A=8\times0 = 0$
$y'_A=8\times2=16$
So $A'=(0,16)$.

Step3: Find new coordinates of point B

Given $B=(3, - 2)$ and $k = 8$.
$x'_B=8\times3 = 24$
$y'_B=8\times(-2)=-16$
So $B'=(24,-16)$.

Step4: Find new coordinates of point C

Given $C=(-1,-4)$ and $k = 8$.
$x'_C=8\times(-1)=-8$
$y'_C=8\times(-4)=-32$
So $C'=(-8,-32)$.

Answer:

$A'=(0,16)$
$B'=(24,-16)$
$C'=(-8,-32)$