Question

Find the equation of the bisector of the angles between the coordinate axes in the first quadrant.

Answer 1

Let P(x, y) be a point on the required bisector in the first quadrant,

The distance of P from the x‑axis is ‘y’ and from the y‑axis is ‘x’.

In the first quadrant, x > 0 and y > 0,

So these distances are y and x, respectively,

Points on the angle bisector are equidistant from the two sides,

∴ y = x

Hence, the equation of the bisector in the first quadrant is y = x.