find the distance between the points of the triangle A(2,1) B(-1,4) and C(-4,3).

I believe that you need to find the length of the sides of
the triangle ABC.

Given the vertices's A(2,1), B(-1,4), and
C(-4,3).

Let us use the distance formula to find the length
of the sides AB, BC, and AC.

==> AB = sqrt( xA-xB)^2
+ (yA-yB)^2

            = sqrt(2+1)^2 + (1-4)^2 = sqrt(3^2
+ -3^2)

           = sqrt(18) =
3sqrt2

==> AB =
3sqrt2.

==> AC = sqrt(xA-xC)^2 +
(yA-yC)^2

              = sqrt(2+4)^2 + (
1-3)^2

              = sqrt(6^2 +
-2^2)

              = sqrt(36+ 4) = sqrt40.=
2sqrt10

==> AC =
2sqrt10.

==> BC = sqrt(xB-xC)^2 +
(yB-yC)^2

             = sqrt(-1+4)^2 +
(4-3)^2

            = sqrt(3^2 +
1)

            =
sqrt10.

==> BC =
sqrt10