Find the equation of the bisector of the acute angle formed by the lines 3x-y-5=0 and 3x+4y-12=0.
please help me and show the solution.. thanks!
Write the equations of the lines in form...
and .
Note that the gradient of any line , where is the angle made with the positive axis.
So in the first case:
and so .
In the second case:
, so .
The angle between them is
.
Therefore the gradient of the line is .
Now, work out the point of intersection of the two lines, and you can substitute this point into to find .