Question

The points $A(5,1,1),B(7,4,7),C(1,6,10)$ and $D(-1,3,4)$ are the vertices of a

• A. Parallelogram
• B. Rectangle
• C. Rhombus
• D. Square

Answer 1

The correct option is C Rhombus

Given points are $A(5,1,1),B(7,4,7),C(1,6,10)$ and $D(-1,3,4)$

$AB=\sqrt{4+9+36}=7$

$BC=\sqrt{36+4+9}=7$

$CD=\sqrt{4+9+36}=7$

$AD=\sqrt{36+4+9}=7$

$AC=\sqrt{16+25+81}=\sqrt{122}$

$BD=\sqrt{64+1+9}=\sqrt{74}$

All sides are equal and diagonals are not equal.

Hence, $ABCD$ is a Rhombus.

Hence, option C.