Answer:
36 units
Step-by-step explanation:
Perimeter of the triangle is the total distances between the vertices which can be calculated as follows using distance formula where necessary:
Distance between (-1, -4) and (9, -4):
This can be calculated without using the distance formula.
The distance between both vertices = |9 -(-1)| = 10 units
Distance between (-1, -4) and (4, 8):
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] (-1, -4) = (x_1, y_1) [/tex]
[tex] (4, 8) = (x_2, y_2) [/tex]
[tex] d = \sqrt{(4 -(-1))^2 + (8 - (-4))^2} [/tex]
[tex] d = \sqrt{(5)^2 + (12)^2} [/tex]
[tex] d = \sqrt{25 + 144} = \sqrt{169} [/tex]
[tex] d = 13 units [/tex]
Distance between (9, -4) and (4, 8):
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] (9, -4) = (x_1, y_1) [/tex]
[tex] (4, 8) = (x_2, y_2) [/tex]
[tex] d = \sqrt{(4 - 9)^2 + (8 - (-4))^2} [/tex]
[tex] d = \sqrt{(-5)^2 + (12)^2} [/tex]
[tex] d = \sqrt{25 + 144} = \sqrt{169} [/tex]
[tex] d = 13 units [/tex]
Perimeter = 10 + 13 + 13 = 36 units
