Question

show that the points A(-4,9,6) B(-1,6,6) and C(0,7,10) from a right angled isosceles triangle​

Answer 1

Answer:

first , you should get the 3 lengths in the triangle

the length of AB =

$\sqrt{ {( - 4 + 1)}^{2} + {(9 - 6)}^{2} + {(6 - 6) }^{2} } = 3 \sqrt{2 }$

second you will calculate the length of AC =

$\sqrt{ {( - 4 - 0) }^{2} + {(9 - 7)}^{2} + {(6 - 10)}^{2} } = 6$

third you will calculate the length of BC =

$\sqrt{ {( - 1 - 0)}^{2} + {(6 - 7)}^{2} + {(6 - 10)}^{2} } = 3 \sqrt{2}$

you see here that the length of BC EQUALs the length of AB, so the triangle is isosceles.

second you see here that:

( AC )² = ( AB )² + ( BC )²

so the this right angled triangle.

Thanks ".