Question:
The ratio in which the segment joining \((2,1)\) and \((0,-2)\) is divided by the line \(2x - 3y + 4 = 0\) is
The ratio in which the segment joining \((2,1)\) and \((0,-2)\) is divided by the line \(2x - 3y + 4 = 0\) is
Show Hint
Negative ratio $\Rightarrow$ external division.
Updated On: Apr 15, 2026
- 1:2
- 2:1
- -1:2
- -2:1
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
Use section formula and substitute into line.
Step 1: Let ratio be \(m:n\).
Point: \[ \left(\frac{2m+0n}{m+n}, \frac{m-2n}{m+n}\right) \]
Step 2: Substitute in line.
\[ 2x -3y +4=0 \] \[ \Rightarrow \frac{4m}{m+n} -3\frac{m-2n}{m+n} +4=0 \]
Step 3: Simplify.
\[ 4m -3m +6n +4(m+n)=0 \] \[ 5m +10n=0 \Rightarrow m:n = -2:1 \] \[ \Rightarrow -1:2 \]
Step 1: Let ratio be \(m:n\).
Point: \[ \left(\frac{2m+0n}{m+n}, \frac{m-2n}{m+n}\right) \]
Step 2: Substitute in line.
\[ 2x -3y +4=0 \] \[ \Rightarrow \frac{4m}{m+n} -3\frac{m-2n}{m+n} +4=0 \]
Step 3: Simplify.
\[ 4m -3m +6n +4(m+n)=0 \] \[ 5m +10n=0 \Rightarrow m:n = -2:1 \] \[ \Rightarrow -1:2 \]
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