Question

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

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 $k = 3$.

Step2: Find coordinates of $A'$

For point $A(1,2)$, using the dilation formula: $x'=3\times1 = 3$ and $y'=3\times2=6$. So $A'=(3,6)$.

Step3: Find coordinates of $B'$

For point $B(3, - 1)$, $x'=3\times3 = 9$ and $y'=3\times(-1)=-3$. So $B'=(9,-3)$.

Step4: Find coordinates of $C'$

For point $C(-4,-2)$, $x'=3\times(-4)=-12$ and $y'=3\times(-2)=-6$. So $C'=(-12,-6)$.

Answer:

$A'=(3,6)$
$B'=(9,-3)$
$C'=(-12,-6)$