Question:
The length of intercept of
\[
x+1=0
\]
between the lines
\[
3x+2y=5
\]
and
\[
3x+2y=3
\]
is
The length of intercept of
\[
x+1=0
\]
between the lines
\[
3x+2y=5
\]
and
\[
3x+2y=3
\]
is
Show Hint
To find the intercept cut by two lines on another line, first find their intersection points with the given line and then apply the distance formula.
Updated On: Jun 22, 2026
- \(2\)
- \(1\)
- \(3\)
- \(4\)
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Write the equation of the line.
Given, \[ x+1=0 \] So, \[ x=-1 \] This is a vertical line.
Step 2: Find point of intersection with \[ 3x+2y=5 \]
Substitute \[ x=-1 \] \[ 3(-1)+2y=5 \] \[ -3+2y=5 \] \[ 2y=8 \] \[ y=4 \] Thus, first point is \[ (-1,4) \]
Step 3: Find point of intersection with \[ 3x+2y=3 \]
Again substitute \[ x=-1 \] \[ 3(-1)+2y=3 \] \[ -3+2y=3 \] \[ 2y=6 \] \[ y=3 \] Thus, second point is \[ (-1,3) \]
Step 4: Find the distance between the two points.
Distance between \[ (-1,4) \] and \[ (-1,3) \] is \[ \sqrt{(-1+1)^2+(4-3)^2} \] \[ =\sqrt{0+1} \] \[ =1 \]
Step 5: Final conclusion.
Therefore, the required intercept length is \[ \boxed{1} \]
Given, \[ x+1=0 \] So, \[ x=-1 \] This is a vertical line.
Step 2: Find point of intersection with \[ 3x+2y=5 \]
Substitute \[ x=-1 \] \[ 3(-1)+2y=5 \] \[ -3+2y=5 \] \[ 2y=8 \] \[ y=4 \] Thus, first point is \[ (-1,4) \]
Step 3: Find point of intersection with \[ 3x+2y=3 \]
Again substitute \[ x=-1 \] \[ 3(-1)+2y=3 \] \[ -3+2y=3 \] \[ 2y=6 \] \[ y=3 \] Thus, second point is \[ (-1,3) \]
Step 4: Find the distance between the two points.
Distance between \[ (-1,4) \] and \[ (-1,3) \] is \[ \sqrt{(-1+1)^2+(4-3)^2} \] \[ =\sqrt{0+1} \] \[ =1 \]
Step 5: Final conclusion.
Therefore, the required intercept length is \[ \boxed{1} \]
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