Answer:
B. 21.2
Step-by-step explanation:
Perimeter of ∆ABC = AB + BC + AC
A(-4, 1)
B(-2, 3)
C(3, -4)
✔️Distance between A(-4, 1) and B(-2, 3):
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] AB = \sqrt{(-2 - (-4))^2 + (3 - 1)^2} = \sqrt{(2)^2 + (2)^2)} [/tex]
[tex] AB = \sqrt{4 + 4} [/tex]
[tex] AB = \sqrt{16} [/tex]
AB = 4 units
✔️Distance between B(-2, 3) and C(3, -4):
[tex] BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] BC = \sqrt{(3 - (-2))^2 + (-4 - 3)^2} = \sqrt{(5)^2 + (-7)^2)} [/tex]
[tex] BC = \sqrt{25 + 49} [/tex]
[tex] BC = \sqrt{74} [/tex]
BC = 8.6 units (nearest tenth)
✔️Distance between A(-4, 1) and C(3, -4):
[tex] AC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] AC = \sqrt{(3 - (-4))^2 + (-4 - 1)^2} = \sqrt{(7)^2 + (-5)^2)} [/tex]
[tex] AC = \sqrt{47 + 25} [/tex]
[tex] AC = \sqrt{74} [/tex]
AC = 8.6 units (nearest tenth)
Perimeter of ∆ABC = 4 + 8.6 + 8.6 = 21.2 units
