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Question
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.
Solution
Given, P divides the line segment joining A(−2, 6) and B(3, −4) in the ratio 2 : 3.
Co-ordinates of point P are
`((2 xx 3 + 3 xx (-2))/(2 + 3), (2 xx (-4) + 3 xx 6)/(2 + 3))`
= `((6 - 6)/5, (-8 + 18)/5)`
= (0, 2) = (x1, y1)
Slope of the required line = m = `3/2`
The required equation of the line is given by
y − y1 = m(x − x1)
`y -2 = 3/2 (x - 0)`
2y − 4 = 3x
2y = 3x + 4
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