Q. 114.7( 13 Votes )

Show that the poi

Answer :

Given: The 4 points are A(2, -2), B(8, 4), C(5, 7) and D(-1, 1).


Note: For a quadrilateral to be a rectangle, the opposite sides of the quadrilateral must be equal and the diagonals must be equal as well.


AB


= 6√2 units …..(1)


BC


= 3√2 units …..(2)


CD


= 6√2 units …..(3)


AD


= 3√2 units …..(4)


From equations 1, 2, 3 and 4, we have


AB = CD and BC = AD …..(5)


Also, AC


= 3√10 units


BD


= 3√10 units


Thus, AC = BD …..(6)


From equations 5 and 6, we can conclude that the opposite sides of quadrilateral ABCD are equal and the diagonals of ABCD are equal as well.


Therefore, point A, B, C and D are the angular points of a rectangle.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
RELATED QUESTIONS :

Determine the poiRD Sharma - Mathematics

Let (3, 4, -1) anRD Sharma - Mathematics

The length of theRD Sharma - Mathematics

If P (0, 1, 2), QRD Sharma - Mathematics

Show that the triMathematics - Exemplar

Write the length RD Sharma - Mathematics

If the distance bRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics

Write the coordinRD Sharma - Mathematics