Question

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

Answer 1

The coordinates of D is (1,0)

Explanation:

Given the following points for a parallelogram:

A (X1,Y1), B (X2,Y2), C (X3,Y3) and D (X4,Y4)

We know that that: X2-X1=X3-X4 (1) and Y2-Y1=Y3-Y4 (2)

Given that

A(X1,Y1)=A(-2, 4)

B(X2,Y2)=B(1, 3)

C(X3,Y3)=C(4, -1)

We need to find D (X4,Y4).

Solving equation (1) for X4 we find that:

X4 = X3 + X1 - X2 = 4 -2 -1 = 1

Solving equation (2) for Y4 we find that:

Y4=Y3+Y1-Y2 = -1 + 4 - 3 =0

Then the coordinates of D is: (1, 0).

Answer 2

ANSWER

D(1,0)

EXPLANATION

The given parallelogram has vertices

A(-2, 4), B(1, 3), C(4, -1) and D.

The diagonals are AC and BD.

The midpoint of AC is


`( ( - 2 + 4)/(2) , (4 + - 1)/(2) )`


`= ( 1, (3)/(2) )`

Let coordinates of D be (m,n).

The midpoint of BD


`( ( 1 + m)/(2) , (3 + n)/(2) )`

Since the diagonals of a parallelogram bisect each other, the two midpoints are equal.

This implies that,


`(1 + m)/(2) = 1`


`1 + m = 2`


`m = 2 - 1 = 1`

Also,


`(3 + n)/(2) = (3)/(2)`


`3 + n = 3`


`n = 3 - 3 = 0`

The coordinates of D are (1,0)