Question

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

Answer 1

$\textbf{Given:}$

$\textsf{Vertices of a parallelogram are}$

$\mathsf{A(1,3),\;B(-1,2),\;C(x,4)\;and\;D(2,5)}$

$\textbf{To find:}$

$\textsf{The value of x}$

$\textbf{Solution:}$

$\textsf{We know that,}$

$\boxed{\textsf{Diagonals of parallelogram are bisect each other}}$

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

$\implies\mathsf{\left(\dfrac{1+x}{2},\dfrac{3+4}{2}\right)=\left(\dfrac{-1+2}{2},\dfrac{2+5}{2}\right)}$

$\implies\mathsf{\left(\dfrac{1+x}{2},\dfrac{7}{2}\right)=\left(\dfrac{1}{2},\dfrac{7}{2}\right)}$

$\implies\mathsf{\dfrac{1+x}{2}=\dfrac{1}{2}}$

$\implies\mathsf{1+x=1}$

$\implies\mathsf{x=1-1}$

$\implies\boxed{\mathsf{x=0}}$

$\textbf{Find more:}$

Show that thepoints A (0, 0), B(3, 0),C(4, 1) and D(1, 1) form a parallelogram​

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