Question 6
20 pts
The vertices of a triangle are (3,-2), (5,-8) and (-2, 1). What is the approximate perimeter of the
triangle
O 17
O 33
O 24
042

Answers

Answer 1

Answer:

24

Explanation:

You have to find the distance between two points three times

D = [tex]\sqrt{(x_{1}-x_{2})^2 + (y_{1} - y_{2})^2[/tex]

1. Distance between (3,-2) (5, -8)  =  [tex]\sqrt{(3 - 5)^2+ [-2 - (-8)]^2}[/tex] = [tex]\sqrt{(-2)^2 + (6)^2}[/tex]

                                                    =    [tex]\sqrt{4 + 36}[/tex]  = [tex]\sqrt{40}[/tex]

2. Distance between (5, -8) (-2, 1)   [tex]\sqrt{[5 - (-2)]^2 + (-8- 1)^2 }[/tex] = [tex]\sqrt{(7)^2 + (-9)^2 }[/tex]

                                                   = [tex]\sqrt{49 + 81}[/tex] = [tex]\sqrt{130}[/tex]

3. Distance between (-2, 1)(3, -2) = [tex]\sqrt{(-2 - 3)^ + [1 -(-2)]^2}[/tex] = [tex]\sqrt{(-5)^2 + (3)^2}[/tex]

                                                  = [tex]\sqrt{25 + 9}[/tex] = [tex]\sqrt{34}[/tex]

Perimeter = distance 1 + distance 2 + distance 3

                 =  [tex]\sqrt{40}[/tex] + [tex]\sqrt{130}[/tex] + [tex]\sqrt{34}[/tex]

                 =   6.32 + 11.40 + 5.83

                 =  23.55 ≈ 24

             

                       


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