Question

Verify the points $(0,7,-10)(1,6,-6)$ and $(4,9,-6)$ are the vertices of an isosceles triangle.

Answer 1

$\Rightarrow$ The given points are $A(0,7,-10),B(1,6,-6),C(4,9,-6)$.

$\therefore$ Distance between $A$ and $B$ $=\sqrt{(1-0{)}^2+(6-7{)}^2+(-6+10{)}^2}=\sqrt{18}$

$\Rightarrow$ Similarly distance between $B$ and $C$ $=\sqrt{(4-1{)}^2+(9-6{)}^2+(-6+6{)}^2}=\sqrt{18}$

$\therefore$ It is an isosceles triangle since $AB=BC$