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:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1})^2[/tex]
To get the distance from A to B, we let:
We plug in what we know:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(6-10)^2+(7-(-3))^2} \\ d=10.77 \end{gathered}[/tex]
To get the distance from A to C, we let:
So,
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(9-10)^2+(-5-(-3))^2} \\ d=\sqrt{5} \\ Simplify \\ d=2.24 \end{gathered}[/tex]
To get the distance from B to C, we let:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(9-6)^2+(-5-7)^2} \\ Simplify \\ d=12.37 \end{gathered}[/tex]
Hence, the perimeter of the triangle:
Perimeter = 10.77+2.24+12.37=25.38
Therefore, the answer is 25.38.
