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=$\sqrt{(x2-x1)^2+(y2-y1)^2}$

AB=$\sqrt{(-3+3)^2+(5-1)^2}$

AB=$\sqrt{0^2+4^2}$

AB=4

we do the same thing for AC and BC

AC=$\sqrt{(4+3)^2+(1-1)^2}$

AC=$\sqrt{7^2+0^2}$

AC=7

BC=$\sqrt{(4+3)^2+(1-5)^2}$

BC=$\sqrt{7^2+(-4)^2}$

BC=$\sqrt{49+16}$

BC=$\sqrt{65}$

The perimeter is equal to the sum of the sides

P=AB+AC+BC=4+7+$\sqrt{65}$=11+$\sqrt{65}$