Question

Three vertices of a parallelogram, taken in order, are (−1, −6), (2, −5) and (7, 2). Write the coordinates of its fourth vertex.

Answer 1

Let $A\left(-1,-6\right),B\left(2,-5\right)\mathrm{and}C\left(7,2\right)$ be the vertices of the parallelogram ABCD.
Let the coordinates of D be (x, y).

Since, diagonals of a parallelogram bisect each other,

$$\begin{gathered} \frac{-1+7}{2}=\frac{2+x}{2}\mathrm{and}\frac{-6+2}{2}=\frac{-5+y}{2} \\ \Rightarrow x=4\mathrm{and}y=1 \end{gathered}$$

Hence, the coordinates of the fourth vertex D are (4, 1).