Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of squares.

Asked by Sakshi | 1 year ago |  27

1 Answer

Solution :-

Given:

The points A (3, 3, 3), B (0, 6, 3), C (1, 7, 7) and D (4, 4, 7)

We know that all sides of a square are equal.

By using the formula,

The distance between any two points (a, b, c) and (m, n, o) is given by,

RD Sharma Solutions for Class 11 Maths Chapter 28 – image 30

RD Sharma Solutions for Class 11 Maths Chapter 28 – image 31

RD Sharma Solutions for Class 11 Maths Chapter 28 – image 32

It is clear that,

AB = BC = CD = AD

Quadrilateral formed by ABCD is a square. [Since all sides are equal]

Hence Proved.

Answered by Aaryan | 1 year ago

Related Questions

A(1, 2, 3), B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC. Find the point in which the bisector of the angle ∠BAC meets BC.

Class 11 Maths Introduction to Three Dimensional Geometry View Answer

The mid-points of the sides of a triangle ABC are given by (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Find the coordinates of A, B and C.

Class 11 Maths Introduction to Three Dimensional Geometry View Answer

Find the ratio in which the line segment joining the points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z = 5.

Class 11 Maths Introduction to Three Dimensional Geometry View Answer