Question 463971: A line through the midpoint of and perpendicular to the segment joining points (1,0) and (5,2)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A line through the midpoint of and perpendicular to the segment joining points (1,0) and (5,2)
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standard form for straight line: y=mx+b, m=slope, b=y-intercept
slope of line segment joining points (1,0) and (5,2)
=∆y/∆x=(2-0)/(5-1)=2/4=1/2
y=(1/2)x+b
solving for b using point (5,2)
2=5/2+b
4=5+2b
2b=-1
b=-1/2
equation:y=x/2-1/2
midpoint coordinates of line segment
(5+1)/2,(2+0)/2=(3,1)
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For line perpendicular to line segment, m=-2 (negative reciprocal of slope of line segment)
y=(-2)x+b
Using midpoint coordinates of line segment (3,1) to solve for b,
1=-2*3+b
7=b
Equation:
y=-2x+7
see graph below as visual check on answer
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