Question

. Find the angles of the parallelogram with vertices(1, 2, .3), (3, 5, 7), (2,0,9), (4, 3, 13).​

Answer 1

Answer:

Let A(-1, 0), B(3, 1), C(2, 2) and D(x, y) be the vertices of a parallelogram ABCD taken in order. Since, the diagonals of a parallelogram bisect each other.

∴ Coordinates of the mid-point of AC=Coordinates of the mid-point of BD

⇒(

2

−1+2

,

2

0+2

)=(

2

3+x

,

2

1+y

)

⇒(

2

1

,1)=(

2

3+x

,

2

y+1

)

⇒

2

3+x

=

2

1

and

2

y+1

=1

⇒x=−2andy=1

Hence, the fourth vertex of the parallelogram is (-2, 1)