Question

A (1, -3) B (1, 0) C (4, 2) Parallelogram ABCD has the coordinates: Find the coordinates of point D.

Answer 1

(4,-1)

Explanation:

Given

3 Co-ordinates of a parallelogram ABCD

A=(1,-3)

B=(1,0)

C=(4,2)

D=(a,b)

One of the property of a parallelogram is that the diagonals bisect each other

In this case, AC and BD bisect each other, Therefore the middle point of AC and BD coincide

⇒Mid-point of AC= Mid-point of BD

(mid point of 2 points (x,y) and (k,l) is
`=(((k+x))/(2) ,((l+y))/(2))`)

`(((1+4))/(2) ,((-3+2))/(2))=(((1+a))/(2) ,((0+b))/(2))\\((5)/(2) ,(-1)/(2))=(((1+a))/(2) ,(b)/(2))`

Compare x and y co-ordinates on both sides

⇒
`(5)/(2) =(1+a)/(2)`

a=4

⇒
`(-1)/(2)=(b)/(2) }`

b=-1

Therefore D=(4,-1)