Question

Find the perimeter of the triangle whose vertices are the following specified points in the plane.(10, -3), (6, 7) and (9,-5)

Answer 1

Given:

(10, -3), (6, 7) and (9,-5)

To determine the perimeter of the triangle based on the given vertices, we first draw the triangle as shown below :

Next, we use the distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1))^2`

To get the distance from A to B, we let:

We plug in what we know:

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ d=√((6-10)^2+(7-(-3))^2) \\ d=10.77 \end{gathered}`

To get the distance from A to C, we let:

So,

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ d=√((9-10)^2+(-5-(-3))^2) \\ d=√(5) \\ Simplify \\ d=2.24 \end{gathered}`

To get the distance from B to C, we let:

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ d=√((9-6)^2+(-5-7)^2) \\ Simplify \\ d=12.37 \end{gathered}`

Hence, the perimeter of the triangle:

Perimeter = 10.77+2.24+12.37=25.38

Therefore, the answer is 25.38.