Question

How do you find the perimeter of a triangle whose coordinates are X(0,2), Y(4,-1), Z(-2,-1)?

Answer 1

`11 +sqrt13`

Explanation:

You can use Pythagorus' Theorem (`a^2 + b^2 = c^2`)to find the lengths of the sides.

Therefore the length of side XY is `sqrt((4-0)^2 + ((-1)-2)^2) = sqrt(4^2 + (-3)^2) = sqrt(16 + 9) = sqrt25 = 5`

Side YZ: `sqrt(((-2)-4)^2 + ((-1)-(-1))^2) = sqrt((-6)^2 + 0^2) = sqrt(36) = 6`

Side XZ: `sqrt(((-2)-0)^2 + ((-1)-2)^2) = sqrt((-2)^2 + (-3)^2) = sqrt(4 + 9) = sqrt13`

Perimeter = XY + YZ + XZ = `5 + 6 + sqrt13` = `11 +sqrt13`