167k views
1 vote
Find the perimeter of the triangle whose vertices are the following specified points in the plane.

Find the perimeter of the triangle whose vertices are the following specified points-example-1
User Mrig
by
8.0k points

1 Answer

6 votes

Let A = (1,-5), B = (2,9) and C = (-6,-8). Solve first for AB, BC, and CA.


\begin{gathered} \text{Solve for }\overline{AB} \\ \overline{AB}=\sqrt[]{(1-2)^2+(-5-9)^2} \\ \overline{AB}=\sqrt[]{(-1)^2+(-14)^2} \\ \overline{AB}=\sqrt[]{1+196} \\ \overline{AB}=\sqrt[]{197} \\ \overline{AB}\approx14.04\text{ units} \end{gathered}
\begin{gathered} \text{Solve for }\overline{BC} \\ \text{ }\overline{BC}=\sqrt[]{(2-(-6))^2+(9-(-8))^2} \\ \text{ }\overline{BC}=\sqrt[]{(8)^2+(17)^2} \\ \text{ }\overline{BC}=\sqrt[]{(64)^{}+(289)^{}} \\ \text{ }\overline{BC}=\sqrt[]{353^{}} \\ \overline{BC}\approx18.79\text{ units} \end{gathered}
\begin{gathered} \text{Solve for }\overline{CA} \\ \text{ }\overline{CA}=\sqrt[]{(-6-1)^2+(-8-(-5))^2} \\ \text{ }\overline{CA}=\sqrt[]{(-7)^2+(-3)^2} \\ \text{ }\overline{CA}=\sqrt[]{49+9} \\ \text{ }\overline{CA}=\sqrt[]{58} \\ \text{ }\overline{CA}\approx7.62\text{ units} \end{gathered}

Now solve for Perimeter


\begin{gathered} P=\overline{AB}+\overline{BC}+\overline{CA} \\ P=14.04+18.79+7.62 \\ P=40.45\text{ units} \end{gathered}

Therefore, the perimeter of the triangle whose points in the plane are (1,-5), (2,9) and (-6,-8) is 40.45 units.

User Chandanjha
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories