Q. 64.2( 10 Votes )

<span lang="EN-US

Answer :

Let A(-1, 0), B(3, 1), C(2, 2) and D(x, y) be the vertices of a parallelogram ABCD taken in order.

Since, the diagonals of a parallelogram bisect each other,


Coordinates of the mid-point of AC = Coordinates of the mid-point of BD



As we know the coordinates of A and C both, we find the midpoint AC.


Midpoint of AC:


x- coordinate = (x1 + x2) / 2


= (-1 + 2 ) / 2 = 1/2


y-coordinate = (y1 + y2) / 2


= (0 + 2 ) / 2 = 1


Mid point of AC = ( 1/2 , 1)


As mid point of AC = mid point of BD


Mid point of BD = ( 1/2 , 1)


x- coordinate = (x1 + x2) / 2


= ( x + 3 ) / 2


(x + 3)/2 = 1/2
x + 3 = 1
x = -2


y- coordinate = (y1 + y2)/2


= (y + 1 ) / 2


(y + 1) /2 = 1
y + 1 =2
y=1


The coordinates of the fourth vertex, D are ( -2 , 1 ).


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