Question

dilate △abc with a scale factor of 5. enter the new coordinates. a(-1,1) b(4,0) c(1,-3) a=(?, ) b=(, ) c=(, )

Explanation:

Step1: Recall dilation formula

To dilate a point $(x,y)$ with a scale factor $k$ centered at the origin, the new - point $(x',y')$ is given by $(x',y')=(k\times x,k\times y)$. Here $k = 5$.

Step2: Calculate new coordinates of point A

For point $A(-1,1)$, using the dilation formula $x'=k\times x$ and $y'=k\times y$. Substitute $x=-1$, $y = 1$, and $k = 5$. Then $x'=5\times(-1)=-5$ and $y'=5\times1 = 5$. So $A'=(-5,5)$.

Step3: Calculate new coordinates of point B

For point $B(4,0)$, substitute $x = 4$, $y = 0$, and $k = 5$ into the dilation formula. Then $x'=5\times4=20$ and $y'=5\times0 = 0$. So $B'=(20,0)$.

Step4: Calculate new coordinates of point C

For point $C(1,-3)$, substitute $x = 1$, $y=-3$, and $k = 5$ into the dilation formula. Then $x'=5\times1=5$ and $y'=5\times(-3)=-15$. So $C'=(5,-15)$.

Answer:

$A'=(-5,5)$
$B'=(20,0)$
$C'=(5,-15)$