If the vertices of a parallelogram …

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It is given in the question that, The vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2) Let, the fourth vertices is S (x , y). The parallelogram's PQRS's vertices, listed in order. Because of this, a parallelogram's diagonals are split in half. We know that the diagonals of a parallelogram bisects with each other. ∴   Coordinates of the PR's midpoint = coordinates for QS's midpoint \begin{gathered}(\frac{3-3}{2} ,\frac{4-2}{2} ) = (\frac{-2+x}{2}, \frac{3+y}{2} )\\ (0,1) = (\frac{-2+x}{2}, \frac{3+y}{2} )\end{gathered}(23−3​,24−2​)=(2−2+x​,23+y​)(0,1)=(2−2+x​,23+y​)​ Now, 0 = \frac{-2+x}{2}0=2−2+x​ .............(1) Simplify the equation, \begin{gathered}0 = -2+x\\x=2\end{gathered}0=−2+xx=2​ Again, 1=\frac{3+y}{2}1=23+y​ ...............(2) Simplify the equation, \begin{gathered}1=\frac{3+y}{2}\\2=3+y\\y=-1\end{gathered}1=23+y​2=3+yy=−1​ the coordinates of its fourth vertex S are (2,-1).