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.