Question:
If \(P(a,b)\) is the midpoint of a line segment intercepted between the coordinate axes, then the equation of the line is
If \(P(a,b)\) is the midpoint of a line segment intercepted between the coordinate axes, then the equation of the line is
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If the midpoint of the intercepts is (a, b), the intercepts themselves are 2a and 2b.
Updated On: Nov 12, 2026
- \(x+y=2\)
- \(ax+by=2\)
- \(x+y=2ab\)
- \(\frac{x}{a}+\frac{y}{b}=2\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
Let the line cut the axes at \((p,0)\) and \((0,q)\). Its equation is \(\dfrac{x}{p}+\dfrac{y}{q}=1\).
Step 2: Midpoint condition
Midpoint \(=\left(\dfrac{p}{2},\dfrac{q}{2}\right)=(a,b)\), so \(p=2a\) and \(q=2b\).
Step 3: Substitute
\(\dfrac{x}{2a}+\dfrac{y}{2b}=1\Rightarrow \dfrac{x}{a}+\dfrac{y}{b}=2\).
Final Answer:
The equation of the line is x/a + y/b = 2. \[ \boxed{\text{(D) }\dfrac{x}{a}+\dfrac{y}{b}=2} \]
Let the line cut the axes at \((p,0)\) and \((0,q)\). Its equation is \(\dfrac{x}{p}+\dfrac{y}{q}=1\).
Step 2: Midpoint condition
Midpoint \(=\left(\dfrac{p}{2},\dfrac{q}{2}\right)=(a,b)\), so \(p=2a\) and \(q=2b\).
Step 3: Substitute
\(\dfrac{x}{2a}+\dfrac{y}{2b}=1\Rightarrow \dfrac{x}{a}+\dfrac{y}{b}=2\).
Final Answer:
The equation of the line is x/a + y/b = 2. \[ \boxed{\text{(D) }\dfrac{x}{a}+\dfrac{y}{b}=2} \]
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