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.
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.