Q. 4

# If the lines p1x + q1y = 1, p2x + q2y = 1 and p3x + q3y = 1 be concurrent, show that the points (p1, q1), (p2, q2) and (p3, q3) are collinear.

Given:

p1x + q1y = 1

p2x + q2y = 1

p3x + q3y = 1

To prove:

The points (p1, q1), (p2, q2) and (p3, q3) are collinear.

Concept Used:

If three lines are concurrent then determinant of equation is zero.

Explanation:

The given lines can be written as follows:

p1 x + q1 y – 1 = 0 … (1)

p2 x + q2 y – 1 = 0 … (2)

p3 x + q3 y – 1 = 0 … (3)

It is given that the three lines are concurrent.

Hence proved, This is the condition for the collinearity of the three points, (p1, q1), (p2, q2) and (p3, q3).

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