Question

Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5,6), B(1,-2)and C(3,-2).

Answer 1

Given vertices are A(5,6), B(1,-2) and C(3,-2).

Let the fourth vertex be D(x,y).

We know that diagonals of a parallelogram bisect each other.

Midpoint of BD = Midpoint of AC.

Therefore, the fourth vertex is (7,6).

Hope it helps!

Answer 2

Dear Student,
To solve this question draw xy plane ,means +x and - x axis and y axis.
then according to the question , identify the quadrant of given points.
point A(5,6): I st quadrant
point B(1,-2): IV quadrant
point C(3,-2):IV quadrant
keeping the shape of parallelogram,we can easily find the fourth vertex.
As in B- C points there is a difference of 2 ,so the same difference is in vertex A-D.
hope the solution helps you.