Given the equation of line L, is y = 4.

(1) Write the slope of line L_{2}, if L_{2}, is the bisector of angle O.

(2) Write the co–ordinates of point P.

(3) Find the equation of L_{2}.

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#### Solution

The equation of the line L_{1} is y = 4.

It is given that L_{2} is the bisector of angle O and ∠O = 90˚.

Thus, the line L_{2} makes an angle of 45˚ with the x-axis.

Thus, slope of line L_{2} = tan 45˚ = 1

The line L_{2} passes through (0, 0) and its slope is 1. So, its equation is given by

y – y_{1} = m(x – x_{1})

y – 0 = 1(x – 0)

y = x

Now, the point P is the point of intersection of the lines L_{1} and L_{2}.

Solving the equations y = 4 and x = y, we get x = y = 4

Thus, the coordinates of the point P are (4, 4).

Concept: Equation of a Line

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