what is the perimeter of $ \triangle abc $ with vertices at $ a(-11,4) $, $ b(-7,8) $, and $ c(-4,4) $?
round only your final answer to the nearest tenth.
2.8 units
7 units
5.9 units
17.7 units

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $AB$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $A(-11,4)$ and $B(-7,8)$, $x_1=-11,y_1 = 4,x_2=-7,y_2 = 8$.
$$
\begin{align*}
AB&=\sqrt{(-7+11)^2+(8 - 4)^2}\
&=\sqrt{4^2+4^2}\
&=\sqrt{16 + 16}\
&=\sqrt{32}\
&=4\sqrt{2}\approx5.7
\end{align*}
$$
## Step2: Calculate the length of $BC$
For $B(-7,8)$ and $C(-4,4)$, $x_1=-7,y_1 = 8,x_2=-4,y_2 = 4$.
$$
\begin{align*}
BC&=\sqrt{(-4 + 7)^2+(4 - 8)^2}\
&=\sqrt{3^2+(-4)^2}\
&=\sqrt{9+16}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step3: Calculate the length of $AC$
For $A(-11,4)$ and $C(-4,4)$, $x_1=-11,y_1 = 4,x_2=-4,y_2 = 4$.
$$
\begin{align*}
AC&=\sqrt{(-4+11)^2+(4 - 4)^2}\
&=\sqrt{7^2+0^2}\
&=7
\end{align*}
$$
## Step4: Calculate the perimeter $P$
$P=AB + BC+AC$. Substitute $AB\approx5.7$, $BC = 5$, $AC = 7$
$P\approx5.7+5 + 7=17.7$

# Answer:
$17.7$ units

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(AB\)

Step2: Calculate the length of \(BC\)

Step3: Calculate the length of \(AC\)

Step4: Calculate the perimeter \(P\)

Answer: