Question

Find the equation of the line passing through the origin and which bisects the portion of the line 3x + y = 6 intercepted between the co-ordinate axes.

Answer 1

Let the line 3x + y = 6 intersect X-axis at A and Y-axis at B.

∴ for A, y = 0 in 3x + y = 6

∴ 3x = 6

∴ x = 2

∴ A ≡ (2, 0)

For B, x = 0 in 3x + y = 6

∴ 3(0) + y = 6

∴ y = 6

∴ B ≡ (0, 6)

Let P(x, y) bisects the portion of the line between the co-ordinate axes.

∴ P is the midpoint of AB

∴ P ≡ `((2 + 0)/2, (0 + 6)/2)` = (1, 3)

∴ required line is passing through the origin O(0, 0) and P(1, 3)

Now, equation of the line passing through the points (x₁, y₁) and (x₂, y₂) is

`(y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2 - x_1)`

∴ equation of the required line passing through (0, 0) and (1, 3) is,

`(y - 0)/(x - 0) = (3 - 0)/(1 - 0)` = 3

∴ y = 3x

∴ 3x – y = 0