The equation of the line bisecting the join o | vedclass

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(C) Let the intercepts of the line on the $x$-axis and $y$-axis be $2a$ and $a$ respectively.The equation of the line in intercept form is $\frac{x}{2

Vedclass · Accepted Answer

$x + 2y = 2$

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(C) Let the intercepts of the line on the $x$-axis and $y$-axis be $2a$ and $a$ respectively.The equation of the line in intercept form is $\frac{x}{2a} + \frac{y}{a} = 1$,which simplifies to $x + 2y = 2a$.....$(i)$The line bisects the join of $(3, -4)$ and $(5, 2)$. The midpoint of these points is $(\frac{3+5}{2}, \frac{-4+2}{2}) = (4, -1)$.Since the line passes through $(4, -1)$,we substitute these coordinates into equation $(i)$:$4 + 2(-1) = 2a$$4 - 2 = 2a$$2 = 2a \Rightarrow a = 1$Substituting $a = 1$ into equation $(i)$,we get $x + 2y = 2(1)$,which is $x + 2y = 2$.

The equation of the line bisecting the join of $(3, -4)$ and $(5, 2)$ and having its intercepts on the $x$-axis and the $y$-axis in the ratio $2 : 1$ is

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