verify that triangle ABC whose vetices are A(4,-6), B(3,-2) and C(5,2).

Did you mean to ask that

vetices  A(4,-6), B(3,-2) and C(5,2) represents a triangle ?

If this is the case then find AB = 17   BC = 32  and AC = 65

Here sum of two sides is always greater then the IIi side so the vertices represents a triangle.

Also you can find the area if it comes out to be non zero in that case the points A BC represents a triangle