Question:
If the line \(2 x+y=\mathrm{k}\) passes though the point which divides the line segment joining the points \((1,1)\) and \((2,4)\) internally in the ratio \(3: 2\) then, \((k+1):(k-1)=\)
If the line \(2 x+y=\mathrm{k}\) passes though the point which divides the line segment joining the points \((1,1)\) and \((2,4)\) internally in the ratio \(3: 2\) then, \((k+1):(k-1)=\)
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Find the dividing point with the section formula and put it in the line equation to get k.
Updated On: Nov 13, 2026
- \(\frac{5}{7}\)
- \(\frac{7}{5}\)
- \(\frac{8}{5}\)
- \(\frac{6}{5}\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
The point dividing \((1,1)\) and \((2,4)\) internally in the ratio \(3:2\) is \(\left(\dfrac{3\cdot2+2\cdot1}{5},\dfrac{3\cdot4+2\cdot1}{5}\right)\).
Step 2: Point
This is \(\left(\dfrac{8}{5},\dfrac{14}{5}\right)\).
Step 3: Find k
\(k=2x+y=\dfrac{16}{5}+\dfrac{14}{5}=6\).
Step 4: Ratio
\((k+1):(k-1)=7:5=\dfrac{7}{5}\), option (B).
Final Answer:
The ratio \((k+1):(k-1)\) equals \(\dfrac{7}{5}\). \[ \boxed{\text{(B) }\dfrac{7}{5}} \]
The point dividing \((1,1)\) and \((2,4)\) internally in the ratio \(3:2\) is \(\left(\dfrac{3\cdot2+2\cdot1}{5},\dfrac{3\cdot4+2\cdot1}{5}\right)\).
Step 2: Point
This is \(\left(\dfrac{8}{5},\dfrac{14}{5}\right)\).
Step 3: Find k
\(k=2x+y=\dfrac{16}{5}+\dfrac{14}{5}=6\).
Step 4: Ratio
\((k+1):(k-1)=7:5=\dfrac{7}{5}\), option (B).
Final Answer:
The ratio \((k+1):(k-1)\) equals \(\dfrac{7}{5}\). \[ \boxed{\text{(B) }\dfrac{7}{5}} \]
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