Q. 35.0( 3 Votes )
Prove that the points (2, -1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.
Answer :
To prove:
The points (2, -1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram
To find:
The angle between diagonals of parallelogram.
Assuming:
A(2, − 1), B(0, 2), C(2, 3) and D(4, 0) be the vertices.
Explanation:
Slope of AB
Slope of BC
Slope of CD
Slope of DA
Thus, AB is parallel to CD and BC is parallel to DA.
Therefore, the given points are the vertices of a parallelogram.
Now, let us find the angle between the diagonals AC and BD.
Let m1 and m2 be the slopes of AC and BD, respectively.
∴
∴
Thus, the diagonal AC is parallel to the y-axis.
∴∠ODB
In triangle MND,
∠DMN
Hence proved, the acute angle between the diagonal is .
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 line45 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Parametric Equations of Straight line48 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 0755 mins




















Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation

