Question

addie wants to find the perimeter of triangle abc. she uses the distance formula to determine the length of bc. finish addies calculations. bc = √((-3 - 2)^2+(8 - -4)^2) bc = √((-5)^2+(12)^2) what is the perimeter of triangle abc? round the answer to the nearest tenth, if necessary. a(-3,-4) b(-3,8) c(2,-4)

Explanation:

Step1: Calculate length of BC

\[

$$\begin{align*} BC&=\sqrt{(-3 - 2)^2+(8 - (-4))^2}\\ &=\sqrt{(-5)^2+(12)^2}\\ &=\sqrt{25 + 144}\\ &=\sqrt{169}\\ & = 13 \end{align*}$$

\]

Step2: Calculate length of AB

The \(x\) - coordinates of \(A(-3,-4)\) and \(B(-3,8)\) are the same. So, \(AB=\vert8-(-4)\vert=\vert8 + 4\vert=12\)

Step3: Calculate length of AC

The \(y\) - coordinates of \(A(-3,-4)\) and \(C(2,-4)\) are the same. So, \(AC=\vert2-(-3)\vert=\vert2 + 3\vert=5\)

Step4: Calculate perimeter of \(\triangle ABC\)

Perimeter \(P=AB + BC+AC=12 + 13+5=30\)

Answer:

30