Question

ABCD is a parallelogram whose vertices A and B
have the coordinates (2, 3) and (-2, 1)
respectively. The diagonals of the parallelogram
meet at the origin O. Find the perimeter of the
parallelogram.

Answer 1

Answer:

In a parallelogram ABCD coordinates of A and B are (2,-3) and (-2,1) , the diagonals

AC and BD meet at the origin O(0,0).

we know that diagonals of a parallelogram bisects each other , thus point O(0,0)

is the mid point of diagonals AC and BD . Let the coordinates of C and D are

(h,k) and (p,q) respectively, therefore

(2+h)/2=0 => h=-2. and (-3+k)/2=0 => k= 3 , thus C(-2,3).

Similarly, (-2+p)/2=0 => p=2. and. (1+q)/2=0 => q=-1. thus D(2,-1).

AB=√{(2+2)^2+(-3–1)^2} = √32 = 4√2 units.

BC=√{(-2+2)^2+(1–3)^2}= √4 = 2 units.

Perimeter of the parallelogram ABCD = 2.(AB+BC) = 2.(4√2+2) units.

= 4.(2√2+1) = 4.(2.828+1) = 4×3.828 = 15.312 units.