SOLUTION: A and B are the point (3,-1) and (2,3) respectively.l is the line 8y-2x-3=0.Show that (a) l is perpendicular to AB (b) l passes through the midpoint of AB.

Question 1117478: A and B are the point (3,-1) and (2,3) respectively.l is the line 8y-2x-3=0.Show that (a) l is perpendicular to AB (b) l passes through the midpoint of AB.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A and B are the points (3,-1) and (2,3) respectively.
line AB DATA::
slope = (3--1)/(2-3) = 4/(-1) = -4
mid-pt = ((3+2)/2,(3-1)/2) = (5/2,1)
Equation of AB::
Form:: y = mx + b
Using (2,3) and m = -4, solve for "b"::
3 = (-4)2 + b
b = 11
Eq. AB:: y = -4x+11
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(a) L is the line 8y-2x-3=0.
y = (2x+3)8
slope = 2/8 = 1/4
Conclusion:: Since (1/4)(-4) = -1, AB and L are perpendicular
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(b) Check (5/2,1) in Eq. AB::
1 = -4(5/2)+11
1 = -10+11
1 = 1
Conclusion:: L does pass thru the midpt of AB.
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Cheers,
Stan H.
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Show that (a) l is perpendicular to AB (b) l passes through the midpoint of AB.
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