unit 8: algebraic connections to geometry - copy
determine the perimeter of triangle abc, given the following
points:
a(5, 3) b(-2, 1) c(3, -6)
25.83
24.07
29.22
25.10
graphing calculator

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of side $AB$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(5,3)$ and $B(-2,1)$, $x_1 = 5,y_1 = 3,x_2=-2,y_2 = 1$.
$$
\begin{align*}
AB&=\sqrt{(-2 - 5)^2+(1 - 3)^2}\
&=\sqrt{(-7)^2+(-2)^2}\
&=\sqrt{49 + 4}\
&=\sqrt{53}\approx7.28
\end{align*}
$$
## Step2: Calculate the length of side $BC$
For points $B(-2,1)$ and $C(3,-6)$, $x_1=-2,y_1 = 1,x_2 = 3,y_2=-6$.
$$
\begin{align*}
BC&=\sqrt{(3+ 2)^2+(-6 - 1)^2}\
&=\sqrt{(5)^2+(-7)^2}\
&=\sqrt{25+49}\
&=\sqrt{74}\approx8.60
\end{align*}
$$
## Step3: Calculate the length of side $AC$
For points $A(5,3)$ and $C(3,-6)$, $x_1 = 5,y_1 = 3,x_2 = 3,y_2=-6$.
$$
\begin{align*}
AC&=\sqrt{(3 - 5)^2+(-6 - 3)^2}\
&=\sqrt{(-2)^2+(-9)^2}\
&=\sqrt{4 + 81}\
&=\sqrt{85}\approx9.22
\end{align*}
$$
## Step4: Calculate the perimeter $P$ of $\triangle ABC$
$P=AB + BC+AC$.
$$
\begin{align*}
P&\approx7.28+8.60 + 9.22\
&=25.10
\end{align*}
$$

# Answer:
$25.10$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of side \(AB\)

Step2: Calculate the length of side \(BC\)

Step3: Calculate the length of side \(AC\)

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

Answer: