Question

m1t2 question 2
triangle abc has vertices with coordinates a(2, 5), b(4, 2), and c(2, 2).
(a) 2 pts
① dilate △abc on the coordinate plane using point c as the center of dilation and a scale factor of 3 to form △abc.
② what are the coordinates of points a and b?
a(
,
)
b(
,
)

Explanation:

Step1: Recall dilation formula

If the center of dilation is $(x_0,y_0)$ and the scale - factor is $k$, and a point $(x,y)$ is dilated, the new point $(x',y')$ has coordinates given by $x'=x_0 + k(x - x_0)$ and $y'=y_0 + k(y - y_0)$. Here, $C(2,2)$ is the center of dilation, so $x_0 = 2$ and $y_0 = 2$, and $k = 3$.

Step2: Find coordinates of $A'$

For point $A(2,5)$:
$x_{A'}=2+3(2 - 2)=2$
$y_{A'}=2+3(5 - 2)=2 + 9=11$
So $A'=(2,11)$.

Step3: Find coordinates of $B'$

For point $B(4,2)$:
$x_{B'}=2+3(4 - 2)=2+6 = 8$
$y_{B'}=2+3(2 - 2)=2$
So $B'=(8,2)$.

Answer:

$A'(2,11)$
$B'(8,2)$