SOLUTION: please help me answer this: Find the equation of the bisector of the pair of acute angles formed by the lines 4x+2y=9 and 2x-y=8. Thank you very much!

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Question 1024885: please help me answer this:
Find the equation of the bisector of the pair of acute angles formed by the lines 4x+2y=9 and 2x-y=8.
Thank you very much!
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
we are given two lines, their point-slope forms are
:
y = -2x + 4.5 (red line)
y = 2x - 8 (green line)
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consider the graph of these two lines
:
+graph%28300%2C+200%2C+-2%2C+10%2C+-10%2C+2%2C+-2x%2B4.5%2C+2x-8%29+
:
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the two lines intersect at the point (3.125, -1.75)
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the two lines intersect the x axis at (2.25, 0) and (4, 0)
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each point on the bisector of the acute angle is equidistant from each line so let's consider where the bisector intersects the x axis
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we know that the x coordinate of this point is 2.25 + ((4 - 2.25) / 2) = 3.125 and the midpoint is (3.125, 0)
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we now have two points on the acute angle bisector line
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calculate the slope of the line
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m = (3.125 - 3.125) / (-1.75 - 0) = 0
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we have a vertical line at x = 3.125
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The equation of the acute angle bisector is x = 3.125
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