Question

if δabc 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 (center A)

For dilation with center $(x_c,y_c)$ and scale factor $k$, new coordinate $(x',y')$ is:
$$x' = x_c + k(x - x_c)$$
$$y' = y_c + k(y - y_c)$$
Substitute $x_c=0,y_c=0,k=2,x=3,y=0$:
$x' = 0 + 2(3-0) = 6$
$y' = 0 + 2(0-0) = 0$

Answer:

$(6, 0)$