Question

If the lines \(p_1x+q_1y=1\), \(p_2x+q_2y=1\) and \(p_3x+q_3y=1\) are concurrent, then the points \((p_1,q_1), (p_2,q_2)\) and \((p_3,q_3)\) are

• A. collinear
• B. form an equilateral triangle
• C. form a scalene triangle
• D. form a right angled triangle

Hint:

Concurrent lines \(\Rightarrow\) linear dependence of coefficients.

Answer 1

The Correct Option is A

Step 1: Concurrency implies the determinant of coefficients is zero.
Step 2: Hence \((p_i,q_i)\) satisfy a linear relation.
Step 3: Therefore the points are collinear.