Question

Three vertices of a parallelogram taken in order are (−1, −6), (2, −5) and (7, 2). The fourth vertex is

Options

•  (1, 4)

• (4, 1)

•  (1, 1)

•  (4, 4)

•  (0, 0)

Answer 1

 (4,1)

Let A(−1, −6), B(2, −5) and C(7, 2) be the given vertex. Let D(h, k) be the fourth vertex.
The midpoints of AC and BD are \[\left( 3, - 2 \right) \text { and } \left( \frac{2 + h}{2}, \frac{- 5 + k}{2} \right)\]  respectively.

We know that the diagonals of a parallelogram bisect each other.

\[\therefore 3 = \frac{2 + h}{2} and - 2 = \frac{- 5 + k}{2}\]

\[ \Rightarrow h = 4 \text { and } k = 1\]