Calculate the perimeter of triangle ABC. A(1,1) , B(0,3) , C(1,-1)

The perimeter of the triangle ABC =
AB+BC+CA.

A(1,1) , B(0,3) ,
C(1,-1)

We know that the distance  d between the the points
(x1,y1) and x2,y2) is given by:

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

AB = sqrt((0-1)^2+(3-1)^2} =
sqrt(1+2^2 ) = sqrt5.

BC= sqrt{(1-0)^2+(-1-3)^2} =
sqrt(1+(-4)^2} = sqrt17.

CA = sqrt{(1-1)^2+(1- -1)^2} =
sqrt 4 = 2.

Therefore Perimeter of the triangle ABC =
sqrt5+sqrt17 +2  = 8.26 units.