Question

The angle between the lines $x-2y+3=0$ and $2x+y-4=0$ is:

• A. $0^{\circ}$
• B. $45^{\circ}$
• C. $90^{\circ}$
• D. $60^{\circ}$

Hint:

Lines $ax+by+c=0$ and $bx-ay+k=0$ are always perpendicular.

Answer 1

The Correct Option is C

Step 1: Concept
Check the product of the slopes $m_{1}m_{2}$. If it equals -1, the lines are perpendicular.
Step 2: Analysis
$m_{1} = 1/2$ and $m_{2} = -2$. $m_{1} \times m_{2} = (1/2) \times (-2) = -1$.
Step 3: Conclusion
Since the product of slopes is -1, the angle between the lines is $90^{\circ}$.
Final Answer: (C)