Question 641198


{{{ graph( 600,600, -10, 10, -10, 10, -x+6, 2x/3-2/3) }}}

The slope of the bisecting line is NOT the average of the slopes of the two given lines.

We need to find a point on the line of intersection and its slope. First find the point of intersection of the lines:

{{{2x - 3y = 2}}}
{{{x + y = 6}}}

The point of intersection is P({{{4}}},{{{ 2}}}).

Find the slopes of the given lines.

{{{m1 = tan(alpha) = 2/3}}}

{{{m2 = tan(beta) = -1}}}

Note that for the first line {{{alpha< 45}}}°.
Note that for the second line {{{beta = 135}}}°.

{{{beta - alpha > 90}}}°

Therefore for the bisecting line of the obtuse angle:

{{{m = tan((alpha + beta)/2)}}}

So the bisector of the obtuse angle will be {{{near}}}{{{ vertical}}}.

The equation of the line will be:

{{{y - 2 = m(x -4)}}}