Question

In what ratio does the Y-axis divide the line segment P(– 3, 1) and Q(6, 2)?

Answer 1

Let the line segment PQ be divided by the Y-axis in the ratio k : 1.

Let A be the intersection's point (x, y).

Then, using the section formula,

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

⇒ x = `(6 xx k + (-3) xx 1)/(k + 1)`

⇒ x = `(6k - 3)/(k + 1)`

Now, on Y-axis, x-coordinate = 0

∴ `(6k - 3)/(k + 1)` = 0

⇒ 6k – 3 = 0

⇒ 6k = 3

⇒ k = `3/6 = 1/2`

∴ Ratio = `1/2` : 1 = 1 : 2

As a result, the needed ratio is 1 : 2.