Question

points (-1,0) and (2, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (4, -1) then the coordinates of the fourth vertex are

Answer 1

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Answer 2

The coordinates of the fourth vertex are (-3,3).

Step-by-step explanation:

One property of a parallelogram is the diagonals bisect each other.

The points (-1,0) and (2, 2) are the extremities of a diagonal of a parallelogram and the two extremities of the other diagonal are (4,-1) and (h,k) (Say.).

Therefore, the midpoint of the two pairs of points (-1,0) and (2,2) & (4,-1) and (h,k) will be the same point.

Hence, we can write

$(\frac{- 1 + 2}{2}, \frac{0 + 2}{2}) = (\frac{h + 4}{2}, \frac{k - 1}{2})$

Hence, h + 4 = - 1 + 2 = 1

⇒ h = - 3

And, k - 1 = 2 + 0 = 2

⇒ k = 3

Therefore, the coordinates of the fourth vertex are (-3,3). (Answer)