(A) Let the line intersect the $x$-axis at $(a, 0)$ and the $y$-axis at $(0, b)$.Since the point $(5, 2)$ bisects the segment between these axes,we ha

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(A) Let the line intersect the $x$-axis at $(a, 0)$ and the $y$-axis at $(0, b)$.Since the point $(5, 2)$ bisects the segment between these axes,we have:$\frac{a + 0}{2} = 5 \Rightarrow a = 10$$\frac{0 + b}{2} = 2 \Rightarrow b = 4$Using the intercept form of the line equation,$\frac{x}{a} + \frac{y}{b} = 1$,we get:$\frac{x}{10} + \frac{y}{4} = 1$Multiplying by $20$,we obtain $2x + 5y = 20$.

Class 11 Mathematics Straight Line Slope of line, Equation of line in different forms

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If the intercept made by the line between the axes is bisected at the point $(5, 2)$,then its equation is

A
$2x + 5y = 20$
B
$5x + 2y = 20$
C
$2x - 5y = 20$
D
$5x - 2y = 20$

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Slope of line, Equation of line in different forms

An equation of a line whose segment between the coordinate axes is divided by the point $\left(\frac{1}{2}, \frac{1}{3}\right)$ in the ratio $2: 3$ is

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Three points $P(h, k)$,$Q(x_{1}, y_{1})$ and $R(x_{2}, y_{2})$ lie on a line. Show that $(h-x_{1})(y_{2}-y_{1}) = (k-y_{1})(x_{2}-x_{1})$.

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If the intercept made by the line between the axes is bisected at the point $(5, 2)$,then its equation is

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