Question

Write down the equation of the line whose gradient is `-2/5` and which passes through point P, where P divides the line segement joining A(4, −8) and B(12, 0) in the ratio 3 : 1.

Answer 1

Given, P divides the line segment joining A(4, −8) and B(12, 0) in the ratio 3 : 1. 

Co-ordinates of point P are

`((3 xx 12 + 1 xx 4)/(3 + 1),(3 xx 0 + 1 xx (-8))/(3 + 1))`

= `((36 + 4)/4, (0 - 8)/4)`

= `(40/4, (-8)/4)`

= (10, −2)

Slope = m = `(-2)/5`  ...(Given)

Thus, the required equation of the line is

y − y₁ = m(x − x₁)

`y + 2 =(-2)/5 (x - 10)`

5y + 10 = −2x + 20

2x + 5y = 10