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 = `("m"x_2 + "n"x_1)/("m" + "n")` 

∴ 0 = `(-6"m" + 3"n")/("m" + "n")`

∴ – 6m + 3n = 0

∴ 3n = 6m

∴ `"m"/"n" = 3/6`

∴ `"m"/"n" = 1/2`   ......(i)

∴ m : n = 1 : 2

By section formula,

y =  `("m"y_2 + "n"y_1)/("m" + "n")` 

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

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

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

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

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