Question
Prove by vector method that the line segment joining the mid-points of the diagonals of trapezium is parallel to the parallel sides and equal to help of there difference.
Solution
Let ABCD be a trapezium and 
be the position vectors of A, B, C, D respectively. Let P be the mid-point of diagonal AC and Q be mid-point of diagonal BD.
position vectors of 
respectively
Now, AB || DC
Again,
Now,
∴ PQ is half of the difference of parallel sides.
Hence the result.
be the position vectors of A, B, C, D respectively. Let P be the mid-point of diagonal AC and Q be mid-point of diagonal BD. position vectors of respectivelyNow, AB || DC
Again,
Now,
∴ PQ is half of the difference of parallel sides.
Hence the result.
