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

Explanation

Given points are `A(0,7,-10), B(1,6,-6) and C(4,9,-6) `
We have to show that the points `(0,7,-10), (1,6,-6) and(4,9,-6)` are the vertices of an isosceles triangle.
so, `AB=sqrt((0-1)^2+(7-6)^2+(-10+6)^2)`
`=sqrt((-1)^2+(1)^2+(-4)^2)`
`=sqrt(18)`
similarly `AC=sqrt((0-4)^2+(7-9)^2+(-10+6)^2)`
`=sqrt((-4)^2+(-2)^2+(-4)^2)`
`=sqrt(16+4+16)`
`=sqrt(36)`
similarly `BC=sqrt((1-4)^2+(6-9)^2+(-6+6)^2)`
`=sqrt((-3)^2+(-3)^2+(0)^2)`
`=sqrt(9+9)`
`=sqrt(18)`
we can clearly see that `AB=BC`
Hence It is a isosceles triangle.