Question

Points A(-2, 4), B(1, 3), C(4, -1) and D form a parallelogram. What are the coordinates of D?

Answer 1

Option D for plato users

Explanation:

D. (1, 0)

Answer 2

D (1,0)

Explanation:

Let the coordinates of D be (a,b).

The diagonals of a parallelogram bisect each other.

The midpoint of AC should be the same as the midpoint of BD.

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

`((2)/(2),(3)/(2)) =((1+a)/(2) ,(3+b)/(2))`

Compare corresponding coordinates

This implies that:

`1+a=2`,
`3+b=3`

`a=2-1`,
`b=3-3`

`a=1`,
`b=0`

Therefore the coordinates of D are: (1,0)