Question

The three vertices of a parallelogram taken in order are (- 1, 1), (3, 1)
and (2, 2) respectively. Find the co-ordinates of the fourth vertex.

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)

Answer 2

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.

So, coordinate of the mid point of AC = coordinate of mid point of BD

⇒ [(-1 + 2)/2, (0 + 2)/2] = [(3 + x)/2, (y + 1)/2]

⇒ (1/2, 1) = [(3 + x)/2, (y + 1)/2]

(3 + x)/2 = ½ ⇒ x = - 2

Also (y + 1)/2 = 1 ⇒ y + 1 = 2

⇒ y = 1

The fourth vertex of parallelogram = (- 2, 1).

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