Given the equation of line L, 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.
The equation of the line L1 is y = 4.
It is given that L2 is the bisector of angle O and ∠O = 90˚.
Thus, the line L2 makes an angle of 45˚ with the x-axis.
Thus, slope of line L2 = tan 45˚ = 1
The line L2 passes through (0, 0) and its slope is 1. So, its equation is given by
y – y1 = m(x – x1)
y – 0 = 1(x – 0)
y = x
Now, the point P is the point of intersection of the lines L1 and L2.
Solving the equations y = 4 and x = y, we get x = y = 4
Thus, the coordinates of the point P are (4, 4).