What kind is the triangle ABC, with vertices A(-1,2), B(4,7),C(-3,6)?

To establish the type of triangle we have to check the
measures of it's angles or the length of it's sides.

In
this case, because all we have is the coordinates of the vertices of the triangle, all
we can find out is the values of the length of the triangle's
sides.

[AB] = sqrt
[(xB-xA)^2 +(yB-yA)^2]

[AB] = sqrt [(4+1)^2 +
(7-2)^2]

[AB] =
sqrt(25+25)

[AB] = sqrt
50

[AC] = sqrt
[(-3+1)^2+(6-2)^2]

[AC] = sqrt
(4+16)

[AC] = sqrt 20

[BC] =
sqrt[(-3-4)^2+(6-7)^2]

[BC] = sqrt
(49+1)

[BC] = sqrt
50

Since [AB]=[BC], the type of the triangle
is isosceles.