Question

The vertices of triangle ABC are A(-2, 2), B(6, 2), and C(0, 8). What is its perimeter?

Answer 1

`8+6sqrt2+2sqrt10`

Explanation:

We are essentially finding the distance between these points, and then add them up.
Remember the distance formula:`d=sqrt ((x_2-x_1)^2+(y_2-y_1)^2)`

The distance from points A to B is:
`d=sqrt ((6-(-2))^2+(2-2)^2)`
`d=sqrt (64+0)`
`d=8`

The distance from points B to C is:
`d=sqrt ((0-6)^2+(8-2)^2)`
`d=sqrt (36+36)`
`d=sqrt 72`
`d=6sqrt 2`

The distance from points A to C is:
`d=sqrt ((0-(-2))^2+(8-2)^2)`
`d=sqrt (4+36)`
`d=sqrt 40`
`d=2sqrt 10`

We add'em up.
`8+6sqrt2+2sqrt10` That is your answer!