Consider the line y = x and the line y = 0, both of which go through the origin. They form a 45° angle in the first quadrant. The bisector of this angle is therefore a line with y = mx for its equation. So what’s the value of m? It is tempting to think that it’s ½, but this is not the case.
Recollection: a/b = c/d.
So:
| √2 | = | 1 – y |
| 1 | y |
y√2 = 1 – y
y√2 + y = 1
y(1 + √2) = 1
| y = | 1 | = | 1 | (1 – √2) | = | 1 – √2 | = √2 – 1 |
| 1 + √2 | (1 + √2) | (1 – √2) | 1 – 2 |
So y/1 = m, m = √2 – 1