Question

A parallelogram ABCD has two of its coordinates as A (-2, 2) and B (8, 2). Find its remaining coordinates

Answer 1

Answer:

Step-by-step explanation:

Sol. Let A(1,−2), B(3,6) and C(5,10) be the three vertices of a parallelogram ABCD and let its fourth vertex be D(a,b).

Join AC and BD. Let AC and BD intersect at point O.

We know that the diagonals of a parallelogram bisect each other.

So, O is the midpoint of AC as well as that of BD.

Using Midpoint formula X=(2x1​+x2​​)and Y=(2y1​+y2​​)

A(1,−2)≡(x1​,y1​), C(5,10)≡(x2​,y2​)

Midpoint of AC is (21+5​,2−2+10​​), i.e.,(3,4)

Midpoint of BD is (23+a​,26+b​​)

∴ 23+a​=3 and 26+b​=4

3+a=6 and 6+b=8

a=3 and b=2

Hence, the fourth vertex is D(3,2).