Question

What is the perimeter of the triangle in units of the triangle formed by the points (-3,1), (-3,5), and (4,1)?

Answer 1

let's say

A(-3,1) B(-3,5) C(4,1)

we need to find the perimeter of ABC for that we find each of the sides

AB BC and AC

there is a formula to find the distance between 2 poins

let's say that a point has the structure A(x1,y1) where x=-3 and y=1 and B(x2,y2) where x2=-3 and y2=5

AB=
`√((x2-x1)^2+(y2-y1)^2)`

AB=
`√((-3+3)^2+(5-1)^2)`

AB=
`√(0^2+4^2)`

AB=4

we do the same thing for AC and BC

AC=
`√((4+3)^2+(1-1)^2)`

AC=
`√(7^2+0^2)`

AC=7

BC=
`√((4+3)^2+(1-5)^2)`

BC=
`√(7^2+(-4)^2)`

BC=
`√(49+16)`

BC=
`√(65)`

The perimeter is equal to the sum of the sides

P=AB+AC+BC=4+7+
`√(65)`=11+
`√(65)`