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Chapter 3: Q3P (page 99)

The diagonals of a parallelogram bisect each other.

Short Answer

Expert verified

Parallelogram method of adding vectors aligns the graph as given below.

Hence, the given theorem is proved.

Step by step solution

01

Concept and formula used

Where Aand Bare the vectors that forms the parallelogram,d1andd2are its first and the second diagonals and the pointsm1andm2are the mid points of the first and the second diagonals respectively.

02

Usage of Vector in Geometry

We have

d1=A+Bd2=B-A

Now, let us call the vector from the origin to the point m1J1. And the vector from the origin to the point m2J2. :

J1=d12=A+B2

J2=B-d22=B-B-A2=A+B2

J1=J2=A+B2

This signifies that the midpoints of each diagonal are in the same place in relation to O.

Then the graph should be

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