Question

The points A(4, –2), B(7, 2), C(0,9) and D(x, y) are vertices of a parallelogram taken in order.

Find the coordinates of vertex D.​

Answer 1

$\textbf{Given:}$  

$\textsf{Points of a parallelogram are A(4,-2), B(7,2), C(0,9), D(x,y)}$

$\textbf{To find:}$  

$\textsf{The co-ordinates of vertex D}$

$\textbf{Solution:}$  

$\textsf{We know that,}$  

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

$\textsf{Mid point of diagonal AC = Mid point diagonal BD}$  

$\implies\mathsf{\left(\dfrac{4+0}{2},\dfrac{-2+9}{2}\right)=\left(\dfrac{7+x}{2},\dfrac{2+y}{}\right)}$  

$\implies\mathsf{\left(\dfrac{4}{2},\dfrac{7}{2}\right)=\left(\dfrac{7+x}{2},\dfrac{2+y}{2}\right)}$  

$\implies\mathsf{\left(2,\dfrac{7}{2}\right)=\left(\dfrac{7+x}{2},\dfrac{2+y}{2}\right)}$  

$\implies\mathsf{2=\dfrac{7+x}{2}}$  

$\implies\mathsf{7+x=4}$  

$\implies\mathsf{x=4-7}$  

$\implies\mathsf{x=-3}$  

$\mathsf{and}$  

$\implies\mathsf{\dfrac{7}{2}=\dfrac{2+y}{2}}$  

$\implies\mathsf{7=2+y}$  

$\implies\mathsf{y=7-2}$  

$\implies\mathsf{y=5}$  

$\therefore\underline{\textsf{The co-ordinates of D are (-3,5)}}$  

$\textbf{Find more:}$

$\textbf{Find more:}$

If A(1,3) ,B(-1,2),C(x,4) and D(2,5) are vertices of parallelogram then write the value of x​

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