Question

Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points $(-2,-1),(1,0),(4,3)$ and $(1,2)$ meet.

• A. $(1,1)$
• B. $(1,3)$
• C. $(5,1)$
• D. None of these

Answer 1

Answer: (A)

$(1,1)$

The vertices of parallelogram in order are $A(-2,-1),B(1,0),C(4,3),D(1,2)$.

So the diagonals will be $AC$ and $BD$.

Since the diagonals of a parallelogram bisects each other, so mid-point of

$AC$ or $BD$ will be intersection point of diagonals.

Hence by mid-point theorem, mid-point of $AC$ is

$A(-2,-1)andC(4,3)$

$x=\frac{-2+4}{2}=1$ and $y=\frac{-1+3}{2}=1$.

so $(1,1)$ is required point.