Question

Given equation of line L₁ is y = 4.
(i) Write the slope of line, if L₂ is the bisector of angle O.
(ii) Write the coordinates of point P.
(iii) Find the equation of L₂

Answer 1

Equation of L₁ is y = 4 (given)
(i) As L₂ is bisector of O
⇒ L₂ is inclined at an angle of 45° with XX'
∴ Slope of L₂ = m = tan 45° = 1
(ii) Slope of L₂ = `(4 - 0)/(x - 0)`
⇒ 1 = `(4)/x`
⇒ x = 4
So coordinates of P are (4, 4).
(Since the slope of L₂ is 1, L₂ ⇒ PM  = OM)
(iii) L₂ passes through O(0, 0), P(4, 4) and has slope m = 1
∴ Equation of L₂ is 
y - y₁ = m (x - x₁)
y - 0 = 1 (x - 0)
or y = x
or x - y = 0.