This question is Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
Here Given that:
A Gradient which passes through a point and that point divided a line segment joining two points in a ratio
Find out the equation of the line.
This is the Question Number 26, Exercise 12.1 of M.L Aggarwal.
Deepak BoraNewbie
Write down the equation of the line whose gradient is 3/2 and which passes through P where P divides the line segment joining A (– 2, 6) and B (3, – 4) in the ratio 2 : 3.
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Given, P divides the line segment joining the points A (-2, 6) and B (3, -4) in the ratio 2: 3
So, the co-ordinates of P will be
x = (m1x2 + m2x1)/(m1 + m2)
= (2×3 + 3×(-2))/ (2 + 3)
= (6 – 6)/5
= 0/5 = 0
y = (m1y2 + m2y1)/(m1 + m2)
= (2×(-4) + 3×(6))/ (2 + 3)
= (-8 + 18)/5 = 10/5
= 2
Hence, the co-ordinates of P are (0, 2)
Now, the slope (m) of the line passing through (0, 2) is 3/2
Thus, the equation will be
y – y1 = m (x – x1)
y – 2 = 3/2 (x – 0)
2y – 4 = 3x
⇒ 3x – 2y + 4 = 0