Question

dilate △abc with a scale factor of 7. enter the new coordinates. a=(?, ) b=(, ) c=(, ) a(-3,1) b(4,4) c(0,-4)

Explanation:

Step1: Recall dilation formula

To dilate a point $(x,y)$ with a scale factor $k$ about the origin, the new - point $(x',y')$ is given by $(x',y')=(k\times x,k\times y)$. Here $k = 7$.

Step2: Find new coordinates of point A

For point A with coordinates $(-3,1)$, using the dilation formula:
$x'_A=7\times(-3)=- 21$ and $y'_A=7\times1 = 7$. So $A'=(-21,7)$.

Step3: Find new coordinates of point B

For point B with coordinates $(4,4)$, using the dilation formula:
$x'_B=7\times4 = 28$ and $y'_B=7\times4=28$. So $B'=(28,28)$.

Step4: Find new coordinates of point C

For point C with coordinates $(0,-4)$, using the dilation formula:
$x'_C=7\times0 = 0$ and $y'_C=7\times(-4)=-28$. So $C'=(0,-28)$.

Answer:

$A'=(-21,7)$
$B'=(28,28)$
$C'=(0,-28)$