NCERT Class 11 Mathematics Solutions: Chapter 12 – Introduction to Three Dimensional Geometry Miscellaneous Exercise Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)
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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 .