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

1 Answer
Mar 13, 2018

Answer:

#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#