Q. 214.1( 9 Votes )
A quadrilateral has vertices (4, 1), (1, 7), (– 6, 0) and (– 1, – 9). Show that the mid – points of the sides of this quadrilateral form a parallelogram.
Answer :
Given, A quadrilateral has vertices (4, 1), (1, 7), (– 6, 0) and (– 1, – 9).
To Prove: Mid – Points of the quadrilateral form a parallelogram.
The formula used: Mid point formula = 
Explanation: Let ABCD is a quadrilateral
E is the midpoint of AB
F is the midpoint of BC
G is the midpoint of CD
H is the midpoint of AD
Now, Find the Coordinates of E, F,G and H using midpoint Formula
Coordinate of E = 
Coordinate of F = 
Coordinate of G = 
Coordinate of H = 
Now, EFGH is a parallelogram if the diagonals EG and FH have the same mid – point
Coordinate of mid – point of EG = 
Coordinate of mid – point of FH = 
Since Diagonals are equals then EFGH is a parallelogram.
Hence, EFGH is a parallelogram.
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