Question

The equation of the line passing through the point $(1, 2)$ and perpendicular to the line $x + y + 1 = 0$ is:

• A. $x - y + 1 = 0$
• B. $x + y - 3 = 0$
• C. $x - y - 1 = 0$
• D. $x - y + 2 = 0$

Hint:

Slope of $x+y+1=0$ is $-1$, so the perpendicular slope must be $+1$.

Answer 1

The Correct Option is A

Step 1: Concept
A line perpendicular to $ax + by + c = 0$ is of the form $bx - ay + \lambda = 0$.
Step 2: Analysis
The given line is $1x + 1y + 1 = 0$. The perpendicular line is $1x - 1y + \lambda = 0$. Since it passes through $(1, 2)$, substitute these values: $1(1) - 1(2) + \lambda = 0 \Rightarrow 1 - 2 + \lambda = 0 \Rightarrow \lambda = 1$.
Step 3: Conclusion
The equation is $x - y + 1 = 0$.
Final Answer: (A)