Question:
If \(P(2,7)\) is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of line is
If \(P(2,7)\) is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of line is
Show Hint
The midpoint of the intercepts gives half of each intercept, so use the intercept form of a line.
Updated On: Nov 12, 2026
- \(2x+7y=28\)
- \(2x-7y=28\)
- \(7x+2y=28\)
- \(7x+2y=14\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
If the line meets the axes at \((a,0)\) and \((0,b)\), its midpoint between the axes is \(\left(\dfrac a2,\dfrac b2\right)\).
Step 2: Find the intercepts
\(\dfrac a2=2\) and \(\dfrac b2=7\), so \(a=4\) and \(b=14\).
Step 3: Intercept form
\(\dfrac x4+\dfrac y{14}=1\). Multiplying by 28 gives \(7x+2y=28\).
Step 4: Compare the options
This matches the third option.
Final Answer:
The equation of the line is 7x + 2y = 28. \[ \boxed{\text{(C) }7x+2y=28} \]
If the line meets the axes at \((a,0)\) and \((0,b)\), its midpoint between the axes is \(\left(\dfrac a2,\dfrac b2\right)\).
Step 2: Find the intercepts
\(\dfrac a2=2\) and \(\dfrac b2=7\), so \(a=4\) and \(b=14\).
Step 3: Intercept form
\(\dfrac x4+\dfrac y{14}=1\). Multiplying by 28 gives \(7x+2y=28\).
Step 4: Compare the options
This matches the third option.
Final Answer:
The equation of the line is 7x + 2y = 28. \[ \boxed{\text{(C) }7x+2y=28} \]
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