Alg6.17

Show that the triangle formed by the points(4,4),(3,5) and (-1,-1) is a right angled traingle.

Let the given points be A,B,C are the vertices of the given triangle.

Now finding the distance between the vertices or the length of the sides,

$\bar AB=\sqrt{(4-3)^2+(4-5)^2},\bar BC=\sqrt{(3+1)^2+(5+1)^2},\bar CA=\sqrt{(-1-4)^2+(-1-4)^2}\,$

$\bar AB=\sqrt{2},\bar BC=\sqrt{52},\bar CA=\sqrt{50}\,$

The realation among the three sides is like

$(\bar BC)^2=(\bar AB)^2+(\bar CA)^2\,$

This is the essential condition of a right angled triangle.

Hence the given points form the vertices of a right angled traingle.