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):
![AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](/tpl/images/1059/9312/76df9.png)
![AB = \sqrt{(-2 - (-4))^2 + (3 - 1)^2} = \sqrt{(2)^2 + (2)^2)}](/tpl/images/1059/9312/ea21a.png)
![AB = \sqrt{4 + 4}](/tpl/images/1059/9312/00d73.png)
![AB = \sqrt{16}](/tpl/images/1059/9312/521fb.png)
AB = 4 units
✔️Distance between B(-2, 3) and C(3, -4):
![BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](/tpl/images/1059/9312/fdb7f.png)
![BC = \sqrt{(3 - (-2))^2 + (-4 - 3)^2} = \sqrt{(5)^2 + (-7)^2)}](/tpl/images/1059/9312/19c2f.png)
![BC = \sqrt{25 + 49}](/tpl/images/1059/9312/8139c.png)
![BC = \sqrt{74}](/tpl/images/1059/9312/41284.png)
BC = 8.6 units (nearest tenth)
✔️Distance between A(-4, 1) and C(3, -4):
![AC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](/tpl/images/1059/9312/4b8a1.png)
![AC = \sqrt{(3 - (-4))^2 + (-4 - 1)^2} = \sqrt{(7)^2 + (-5)^2)}](/tpl/images/1059/9312/8d8c0.png)
![AC = \sqrt{47 + 25}](/tpl/images/1059/9312/39bd1.png)
![AC = \sqrt{74}](/tpl/images/1059/9312/5f7ee.png)
AC = 8.6 units (nearest tenth)
Perimeter of ∆ABC = 4 + 8.6 + 8.6 = 21.2 units