Question

2
select the correct answer.
$delta abc$ is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image $delta abc$. if $a = (2, 2)$, $b = (4, 3)$, and $c = (6, 3)$, what is the length of $bc$?
a. 3 units
b. 4 units
c. 2 units
d. 1 unit

Explanation:

Step1: Find length of $BC$

First, calculate the distance between $B(4,3)$ and $C(6,3)$ using the distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

$$\begin{align*} BC&=\sqrt{(6-4)^2+(3-3)^2}\\ &=\sqrt{2^2+0^2}\\ &=\sqrt{4}\\ &=2 \end{align*}$$

Step2: Apply dilation scale factor

Multiply the length of $BC$ by the scale factor $0.5$ to get $B'C'$.
$B'C' = 2 \times 0.5$

Answer:

D. 1 unit