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