Question 332208
find the equation of the bisector of the acute angles and also the equation of the obtuse angles formed by the lines 7x-2y=4 and 3x+5y=15.
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Find the slope of each line:
7x-2y = 4, m = 7/2
3x+5y =15, m = -3/5
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The slope is the tangent of the angle with the x-axis, so the arctan(m) is the angle.
Add the 2 angles, and divide by 2 --> the angle of the bisector.
Angle of bisector = (arctan(7/2) + arctan(-3/5))/2 = 21.5454 degs
The slope is the tangent, m = 0.3948
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Find the intersection of the lines 7x-2y=4 and 3x+5y=15.
It's (50/41,93/41) or (1.2195,2.2683)
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Use the point and y = mx+b to find b
2.2683 = 0.3948*1.2195 + b
b = 1.7868
Equation of the bisector:  y = 0.3948x + 1.7868
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I don't what you mean by "the equation of the obtuse angles"