Question

Find the ratio in which Y-axis divides the point A(3, 5) and point B(–6, 7). Find the coordinates of the point.

Answer 1

Let C be a point on Y-axis which divides seg AB in the ratio m : n.

Point C lies on the Y-axis.

∴ Its X-coordinate is 0.

Let C = (0, y)

Here,

A(x₁, y₁) = A(3, 5)

B(x₂, y₂) = B(–6, 7)

By Section formula,

`x = (mx_2 + nx_1)/(m + n)` 

∴ `0 = (-6m + 3n)/(m + n)`

∴ –6m + 3n = 0

∴ 3n = 6m

∴ `m/n = 3/6`

∴ `m/n = 1/2`   ...(i)

∴ m : n = 1 : 2

By section formula,

`y =  (my_2 + ny_1)/(m + n)` 

`y = (7m + 5n)/(m + n)`

= `(7m + 5(2m))/(m + 2m)`   ...[From (i), n = 2m]

= `(7m + 10m)/(3m)`

= `(17m)/(3m)`

∴ Y-axis divides the seg AB in the ratio 1 : 2 and the co-ordinates of that point is `(0, 17/3)`.