Question

The length of intercept of \[ x+1=0 \] between the lines \[ 3x+2y=5 \] and \[ 3x+2y=3 \] is

• A. \(2\)
• B. \(1\)
• C. \(3\)
• D. \(4\)

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.

Answer 1

The Correct Option is B

Step 1: Identify the intercepting line.
The line $x+1=0$ simplifies to $x=-1$, a vertical line parallel to the $y$-axis.
Step 2: Intersect $x=-1$ with $3x+2y=5$.
$-3+2y=5 \implies y=4$. First intersection: $(-1,\,4)$.
Step 3: Intersect $x=-1$ with $3x+2y=3$.
$-3+2y=3 \implies y=3$. Second intersection: $(-1,\,3)$.
Step 4: Compute the intercept length.
\[\text{Length}=|4-3|=1.\]
Step 5: Interpret the result.
The vertical line $x=-1$ cuts a segment of length 1 between the two parallel lines.
Step 6: State the answer.
\[ \boxed{1} \]