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!

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- Feb 20th 2010, 12:05 AMlanceBisector
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! - Feb 20th 2010, 12:38 AMProve It
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 .