Question

Without using Pythagoras theorem, show that `A(4,4), B(3,5)a n d C(-1,-1)` are the vertices of a right angled triangle.

Answer 1

Let A(4,4), B(3,5) and C(-1,-1) be the vertices of `triangle ABC`.
Let `m_(1) and m_(2)` be the slopes of AB and AC respectively. Then,
`m_(1)="slopes of AB"=((5-4))/((3-4))=-1`

`m_(2)="slopes of AC"=((-1-4))/((-1-4))=(-5)/(-5)=1`
`therefore m_(1)m_(2)=-1`
So, AB CD and therefore, `angleCAD=90^(@)`
Hence, the given points are the vertices of a right trigangle.