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Question
If the point (5, 2) bisects the intercept of a line between the axes, then its equation is
Options
5x + 2y = 20
2x + 5y = 20
5x − 2y = 20
2x − 5y = 20
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Solution
2x + 5y = 20
Let the equation of the line be \[\frac{x}{a} + \frac{y}{b} = 1\]
The coordinates of the intersection of this line with the coordinate axes are (a, 0) and (0, b).
The midpoint of (a, 0) and (0, b) is \[\left( \frac{a}{2}, \frac{b}{2} \right)\]
According to the question:
\[\left( \frac{a}{2}, \frac{b}{2} \right) = \left( 5, 2 \right)\]
\[ \Rightarrow \frac{a}{2} = 5, \frac{b}{2} = 2\]
\[ \Rightarrow a = 10, b = 4\]
The equation of the required line is given below:
\[\frac{x}{10} + \frac{y}{4} = 1\]
\[ \Rightarrow 2x + 5y = 20\]
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