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.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of lineVarious Forms of Equations of lineVarious Forms of Equations of line45 mins
Slope, inclination and angle between two linesSlope, inclination and angle between two linesSlope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of lineInteractive Quiz on Equations of lineInteractive Quiz on Equations of line23 mins
Parametric Equations of Straight lineParametric Equations of Straight lineParametric Equations of Straight line48 mins
Straight line | Analyse your learning through quizStraight line | Analyse your learning through quizStraight line | Analyse your learning through quiz56 mins
General Equation of a lineGeneral Equation of a lineGeneral Equation of a line43 mins
Motion in a Straight Line - 06Motion in a Straight Line - 06Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 05Motion in a Straight Line - 05Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 03Motion in a Straight Line - 03Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 07Motion in a Straight Line - 07Motion in a Straight Line - 0755 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses