Question

The ratio in which the x-axis divides the line segment joining the points A (a₁, b₁) and B (a₂, b₂) is

Options

• b₁ : b₂

• −b₁ : b₂

• a₁ : a₂

• −a₁ : a₂

Answer 1

−b₁ : b₂ 

Explanation;

Hint:

A line divides internally in the ratio m : n the point P is, `(("m"x_2 + "n"x_1)/("m" + "n"), ("m"_2 +"n"y_1)/("m" + "n"))`

The point P is (a, 0) = `(("ma"_2 + "na"_1)/("m" + "n"), ("mb"_2 + "nb"_1)/("m"  "n"))`

∴ `("mb"_2 + "nb"_1)/("m" + "n")` = 0

mb₂ + nb₁ = 0

⇒ mb₂ = −nb₁

`"m"/"n" = "b"_1/"b"_2`

∴ m : n = −b₁ : b₂