Question

In what ratio does the x-axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Find the coordinates of the point of division.

Answer 1

Let the ratio in which x-axis divides the line segment joining (– 4, – 6) and (–1, 7) = 1 : k

Then,

x-coordinate becomes `(-1 - 4k)/(k + 1)`

y-coordinate becomes `(7 - 6k)/(k + 1)`

Since P lies on x-axis, y coordinate = 0

`(7 - 6k)/(k + 1)` = 0

7 – 6k = 0

k = `6/7`

Now, m₁ = 6 and m₂ = 7

By using section formula,

x = `(m_1x_2 + m_2x_1)/(m_1 + m_2)`

= `(6(-1) + 7(-4))/(6 + 7)`

= `(-6 - 28)/13`

= `(-34)/13`

So, now

y = `(6(7) + 7(-6))/(6 + 7)`

= `(42 - 42)/13`

= 0

Hence, the coordinates of P are `((-34)/13, 0)`