Question

If A(2,0) , B(6,2) ,C (x,5) & D(0,3)  are the vertices of a parallelogram and (m, n) is the point of intersection of its diagonals , then which relation is correct ?​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{A(2,0) , B(6,2) ,C (x,5) and D(0,3)  are the vertices of a parallelogram}$

$\underline{\textbf{To find:}}$

$\textsf{Point of intersection of diagonals}$

$\underline{\textbf{Solution:}}$

$\textsf{We know that,}$

$\textbf{"Diagonals of parallelogram bisect each other"}$

$\implies\textbf{Midpoint of diagonal AC = Midpoint of diagonal BD}$

$\implies\textsf{Point ofintersection of diagonals}$

$\textsf{= Midpoint of diagonal BD}$

$\mathsf{=\left(\dfrac{6+0}{2},\dfrac{2+3}{2}\right)}$

$\mathsf{=\left(3,\dfrac{5}{2}\right)}$

$\therefore\mathsf{Point\;of\;intersection\;of\;diagonals\;is\;\left(3,\dfrac{5}{2}\right)}$