Question

A(−10, −2) and B(2, 10) are two end points of a line segment. If AB intersects the x-axis at P, find the:

1.  ratio in which ‘P’ divides AB.
2. coordinates of point P.

Answer 1

(a) Given: A(−10, −2) and B(2, 10) are two end points of a line segment.

y₁ = −2

y₂ = 10

x₁ = −10

x₂ = 2

Let the point at which AB intersects the x-axis be P(x, 0), and P divides AB in the ratio m : n.

Using the section formula,

`y = (my_2 + ny_1)/(m + n)`

Substituting values, we get:

⇒ 0 = `(m xx 10 + n xx (-2))/(m + n)`

⇒ 0 = `(10m - 2)/(m + n)`

⇒ 10m − 2n = 0

⇒ 10m = 2n

⇒ `m/n = 2/10`

⇒ `m/n = 1/5`

⇒ m : n = 1 : 5

(b) Using the section formula,

x = `(mx_2 - nx_1)/(m + n)`

Substituting values, we get:

⇒ x = `(1 xx 2 + 5 xx -10)/(1 + 5)`

⇒ x = `(2 - 50)/6`

⇒ x = `(-48)/6`

⇒ x = −8

Hence, the coordinates of point P are (−8, 0).