# NCERT Class 11 Mathematics Solutions: Chapter 12 –Introduction to Three Dimensional Geometry Miscellaneous Exercise Part 1

Get unlimited access to the best preparation resource for IMO : fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 142K) ↧

1. Three vertices of a parallelogram are . Find the coordinates of the fourth vertex.

Answer:

The three vertices of a parallelogram are given as .

Consider the coordinates of the fourth vertex be .

We know that the diagonals of a parallelogram bisect each other.

So, in parallelogram bisect each other.

So, the coordinates of the fourth vertex are .

2. Find the lengths of the medians of the triangle with vertices

Answer:

Consider be the medians of the given triangle .

Since is the median, is the mid-point of .

Coordinates of point

Since is the median, is the mid-point of

Coordinates of point

Since is the median, is the-point of .

Coordinates of point

Length of

So, the length of the medians of are .