This is the Important question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD.

Here you have to find the equation of the line passing through the points P (5, 1) and Q (1, – 1).

Hence, you show that the points P, Q and R (11, 4) are collinear.

This is the Question Number 19 Exercise 12.1 of M.L Aggarwal.

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# Find the equation of the line passing through the points P (5, 1) and Q (1, – 1). Hence, show that the points P, Q and R (11, 4) are collinear.

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Given, two points P (5, 1) and G (1, -1)

Slope of the line (m) = y

_{2}– y_{1}/ x_{2}– x_{1}= -1 – 1/ 1 – 5

= -2/-4 = ½

So, the equation of the line is

y – y

_{1}= m (x – x_{1})y – 1 = ½ (x – 5)

2y – 2 = x – 5

x – 2y – 3 = 0

Now, if point R (11, 4) is collinear to points P and Q then, R (11, 4) should satisfy the line equation

On substituting, we have

11 – 2(4) – 3 = 11 – 8 – 3 = 0

As point R satisfies the line equation,

Hence, P, Q and R are collinear.