Question

Three vertices of a parallelogram are shown in the figure below.Give the coordinates of the fourth vertex.(-4,2)(6,-5)(3, -11)

Answer 1

`\begin{gathered} In\text{ a parallelogram diagonals bisects each other} \\ \text{hence midpoint of }BD\text{ = midpoint of AC} \\ A=(-4,2) \\ B=(6,-5) \\ C=(3,-11) \end{gathered}`
`\begin{gathered} ((-4+3)/(2),(2-11)/(2))=((6+x)/(2),(-5+y)/(2)) \\ \text{hence} \end{gathered}`
`\begin{gathered} ((-1)/(2),(-9)/(2))=((6+x)/(2),(-5+y)/(2)) \\ \text{this implies that} \\ 6+x=-1 \\ \text{and} \\ -5+y=-9 \\ \text{therefore} \\ x=-1-6\Rightarrow x=-7 \\ y=-9+5\Rightarrow x=-4 \\ \text{hence the vertex is at (-7,-4)} \end{gathered}`