Question 1185926: Find the bisector of the obtuse angle between the lines 11x +2y + 7 = 0 and x + 2y + 20 = 0
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the bisector of the obtuse angle between the lines 11x +2y + 7 = 0 and x + 2y + 20 = 0
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Step 1, find the intersection:
11x +2y + 7 = 0
x + 2y + 20 = 0
---------------------------- Subtract
10x - 13 = 0
x = 1.3
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x + 2y + 20 = 0
1.3 + 2y = -20
y = -10.65
(1.3,-10.65) is the intersection
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Find the slope of each line:
11x +2y + 7 = 0
m1 = -11/2
x + 2y + 20 = 0
m2 = -1/2
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The angle with the x-axis is the inverse tangent of the slope.
Find the average of the 2 angles.
The slope of the bisector is the tangent of the average of the 2 angles.
Slope = 0.75
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The bisector is the line with slope = 0.75 thru (1.3,-10.65)
y+10.65 = 0.75*(x-1.3)
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Post a TY note and I'll send you a graph.
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