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.

Answer 1

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