Question

The vertices of a parallelogram are $(3,-2),(4,0),(6,-3)$ and $(5,-5)$. The diagonals intersect at the point $M$. The coordinates of the point $M$ are:

• A. $(\frac{9}{2},-\frac{5}{2})$
• B. $(\frac{7}{2},-\frac{5}{2})$
• C. $(\frac{7}{2},-\frac{3}{2})$
• D. None of these

Answer 1

The correct option is A

$(\frac{9}{2},-\frac{5}{2})$

The diagonals of a parallelogram bisect each other. Hence $M$ is the midpoint of the opposite vertices $(3,-2),(6,-3)$ or of the opposite vertices $(4,0),(5,-5)$
Midpoint of two points ${(x}_1,y_1)$ and ${(x}_2,y_2)$ is calculated by the formula $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}).$
Using this formula, mid point of $(3,-2),(6,-3)$ will be,

$\Rightarrow (\frac{3+6}{2},\frac{-2-3}{2})$

$\Rightarrow (\frac{9}{2},-\frac{5}{2})$