Calculate the perimeter of the triangle whose vertices are (1,2) (-1,4) and * (-2,3).

Let ABC be a triangle.

Given
the vertices's of a triangle are:

A(1,2) , B(-1,4), and
C(-2,3).

We need to find the perimeter of the
triangle.

First we need to find the length of the
sides.

==> AB = sqrt[( 1+1)^2 + (
2-4)^2)

            = sqrt( 2^2 + 2^2
)

            = sqrt(
4+4)

             =
sqrt8

==> AB =
2sqrt2.

==> AC = sqrt( 1+ 2)^2 + (
2-3)^2

              = sqrt( 3^2 +
1^2)

                = sqrt(9+
1)

                =
sqrt10.

==> AC=
sqrt10.

==> BC = sqrt( -1+2)^2
+(4-3)^2]

             = sqrt( 1^2 + 1^2
)

            =
sqrt2

==> BC =
sqrt2.

==> The
perimeter of the triangle
is:

P = AB + AC +
BC

   = 2sqrt2 + sqrt10 +
sqrt2

   = 7.4 units. (
approx.)