Show that the points A(2,3,5),B(-4,7,-7),C(-2,1,-10) and D(4,-3,2) are the vertices of a rectangle.

Answer

N/a

Explanation

`AB=sqrt(( -4-2)^(2)+(7-3)^(2)+(-7-5)^(2))`
`=sqrt(36+16+144)=14` units
`BC=sqrt((-2+4)^(2)+(1-7)^(2)+(-10+7)^(2))`
`=sqrt(4+36+9)=7` units
`CD=sqrt((4+2)^(2)+(-3-1)^(2)+(2+10)^(2))`
`=sqrt(36+16+144)=14` units
`DA=sqrt((2-4)^(2)+(3+3)^(2)+(5-2)^(2))`
`=sqrt(4+36+9)=7` units
`AC=sqrt((-2-2)^(2)+(1-3)^(2)+(-10-5)^(2))`
`=sqrt(16+4+225)=7sqrt(5) `units
and `BD = sqrt((4+4)^(2)+(-3-7)^(2)+(2+7)^(2))`
`=sqrt(64+100+81)=7sqrt(5) units`
`because AB=CD`
BC=DA
and AC=BD
`therefore ABCD` is a rectangle.