Question

Show that the point $A(-4,9,6)B(-1,7,10)$ and $C(0,7,10)$ form a right angled isosceles triangle.

Answer 1

$AB=\sqrt{(-1+4{)}^2+(7-9{)}^2+(10-6{)}^2}=\sqrt{9+4+16}=\sqrt{29}BC=\sqrt{(0+1{)}^2+(7-7{)}^2+(10-10{)}^2}=1AC=\sqrt{(0+4{)}^2+(7-9{)}^2+(10-6{)}^2}=\sqrt{16+4+16}=\sqrt{36}$

$⟹$ all the three sides $AB,BC$ and $AC$ are different and hence it is not an isosceles triangle

Moreover, Pythagoras theorem can be applied here and hence it is not a right angled triangle as well.