Question

warm-up
what are the side lengths of triangle abc?
type the correct answer in each box. if necessary, round any decimal to the nearest tenth.

Explanation:

Step1: Identify coordinates of vertices

From the graph: $A=(2, 6)$, $B=(6, 2)$, $C=(2, -6)$

Step2: Calculate length of AB

Use distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$$\begin{align*} AB&=\sqrt{(6-2)^2+(2-6)^2}\\ &=\sqrt{4^2+(-4)^2}\\ &=\sqrt{16+16}\\ &=\sqrt{32}\\ &=4\sqrt{2}\approx5.7 \end{align*}$$

Step3: Calculate length of BC

Apply distance formula to B and C

$$\begin{align*} BC&=\sqrt{(2-6)^2+(-6-2)^2}\\ &=\sqrt{(-4)^2+(-8)^2}\\ &=\sqrt{16+64}\\ &=\sqrt{80}\\ &=4\sqrt{5}\approx8.9 \end{align*}$$

Step4: Calculate length of AC

Apply distance formula to A and C

$$\begin{align*} AC&=\sqrt{(2-2)^2+(-6-6)^2}\\ &=\sqrt{0^2+(-12)^2}\\ &=\sqrt{144}\\ &=12 \end{align*}$$

Answer:

$AB\approx5.7$, $BC\approx8.9$, $AC=12$