Question

if $\triangle abc$ is dilated by a scale factor of 2 with a dilation center of $a$, what will be the coordinates of point $b$?

Explanation:

Step1: Identify coordinates of A and B

From the graph: $A=(0,0)$, $B=(3,0)$

Step2: Apply dilation formula

For dilation centered at $A(x_A,y_A)$ with scale factor $k$, the new coordinate $B'(x',y')$ is calculated as:
$x' = x_A + k(x_B - x_A)$
$y' = y_A + k(y_B - y_A)$
Substitute $k=2$, $x_A=0,y_A=0$, $x_B=3,y_B=0$:
$x' = 0 + 2(3-0) = 6$
$y' = 0 + 2(0-0) = 0$

Answer:

$(6, 0)$