Question

Given equation of line L₁ is y = 4.

1. Write the slope of line L₂ if L₂ is the bisector of angle O.
2. Write the co-ordinates of point P.
3. Find the equation of L₂.

Answer 1

i. Equation of line L₁ is y = 4

∵ L₂ is the bisector of ∠O

∴ ∠POX = 45°

Slope = tan 45° = 1   ...(i)

Let coordinates of P be (x, y)

∵ P lies on L₁

ii.  ∴ Slope of L₂ = `(y_2 - y_1)/(x_2 -x_1)`

 `1 = (4 - 0)/(x - 0)`

`=> 1 = 4/x`    ...(ii)

From equation (i) and (ii)

`1 = 4/x`

`=>` x = 4

∴ Coordinates of P are (4, 4)

iii. Equation of L₂ is

y – y₁ = m(x – x₁)

`=>` y – 4 = 1(x – 4)

`=>` y – 4 = x – 4

`=>` x = y