Question

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

Answer 1

Answer: The coordinates of D are (1,0).

Step-by-step explanation:

Given : The vertices of parallelogram are A(-2, 4), B(1, 3), C(4, -1) and D.

Let the fourth vertex be D(x,y).

We know that the diagonal of parallelogram bisects each other.

i.e.  Mid points of AC = Mid point of BD [ where AC and BD are diagonals of parallelogram ]

i.e.

$(\dfrac{-2+4}{2},\dfrac{4-1}{2})=(\dfrac{1+x}{2},\dfrac{3+y}{2})\\\\\Rightarrow\ (1,\dfrac{3}{2})=(\dfrac{1+x}{2},\dfrac{3+y}{2})\\\\\Rightarrow\ \dfrac{1+x}{2}=1\ \ \ \ , \ \dfrac{3+y}{2}=\dfrac{3}{2}\\\\\Rightarrow\ 1+x=2\ ,\ \ \ 3+y=3\\\\\Rightarropw\ x=1\ \ ,\ \ y=0$

Hence, the coordinates of D are (1,0).

Answer 2

After some work I concluded that the coordinates to D are (-2,0)