Question

26. Find the perimeter of LABC with vertices A(-5, -2), B(-2,-2), and C(-5,2).

a.12 units
b. 7 units
c. 32 units
d. 14 units

I know the is 12 but I need help understanding the math to get to 12 if anyone can explain it that would be great

Answer 1

We know that ABC is a triangle and if its a triangle every vertice conects to the other 2 vertices

So we can do the distance between AB, AC and BC then sum them

dAB =
`√((x_a-x_b)^2+(y_a-y_b)^2)`

dAB =
`√((-5-(-2))^2+(-2-(-2))^2)`

dAB =
`√((-3)^2+0^2)`

dAB = 3

dAC =
`√((-5-(-5))^2+(-2-2)^2)`

dAC =
`√(0^2+(-4)^2)`

dAC = 4

dBC =
`\sqrt{(-2-(-5))^2+(-2-2)^2`

dBC =
`√(3^2+(-4)^2)`

dBC =
`√(9 + 16)`

dBC =
`√(25)`

dBC = 5

3 + 4 + 5 = 12

So alternative A.