Question

Calculate the perimeter of the triangle formed by the following set of vertices. {(−1,4),(−2,3),(0,2)}

Answer 1

From the problem, we have the vertices of the triangle :

`(-1,4),(-2,3),(0,2)`

We need to find the distances between these vertices.

Perimeter is the sum of all sides of the triangle.

Using distance formula :

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

The distances are :

`\begin{gathered} d_1=\sqrt[]{(-2+1)^2+(3-4)^2}=\sqrt[]{2} \\ d_2=\sqrt[]{(0+1)^2+(2-4)^2}=\sqrt[]{5} \\ d_3=\sqrt[]{(0+2)^2+(2-3)^2}=\sqrt[]{5} \end{gathered}`

Take the sum of the distances :

`\begin{gathered} P=\sqrt[]{2}+\sqrt[]{5}+\sqrt[]{5} \\ P=\sqrt[]{2}+2\sqrt[]{5}\quad or\quad 5.89 \end{gathered}`

ANSWER :

P = (√2 + 2√5) units or 5.89 units