First slide

Introduction to 3-D Geometry

Question

The coplanar points $(3, 2, 5), (2, 1, 1), (- 1, 4, 1), (0, 5, 5)$ form a

Very Easy

A

Parallelogram
B

Square
C

rhombus
D

rectangle

Solution

Given points are $A (3, 2, 5), B (2, 1, 1), C (- 1, 4, 1), D (0, 5, 5)$
The lengths of the sides
$\begin{matrix} A B = \sqrt{1 + 1 + 16} = \sqrt{18} \\ B C = \sqrt{9 + 9 + 0} = \sqrt{18} \\ A C = \sqrt{16 + 4 + 16} = \sqrt{36} \\ B D = \sqrt{4 + 16 + 16} = \sqrt{36} \end{matrix}$
Observing the adjacent sides $A B, B C$ are equal, and the lengths of the diagonal are equal
Diagonals are equal, and adjacent sides are equal
Therefore, the quadrilateral formed by the given vertices is square.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App