Question

Without using Pythagoras theorem show that the points A(1,2),B(4,5) and C(6,3) are the vertices of a right angled triangle

Answer 1

here,
eq. of AB-x-y+1=0----(1)
eq.of BC-x+y-9=0----(2)
In (1),Coefficient of x=Coefficient of y in (2)
Also,coefficient of y in (1)=coefficient of x in (2)
Hence,the two line segments r perpendicular to each other.
so,ABC is a rt. angled triangle.