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) = y2 – y1/ x2 – x1
= -1 – 1/ 1 – 5
= -2/-4 = ½
So, the equation of the line is
y – y1 = m (x – x1)
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.