SOLUTION: The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).

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Question 1109398: The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,0) and (5,-2)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (1,0) and (x%5B2%5D,y%5B2%5D) is the second point (5,-2))


m=%28-2-0%29%2F%285-1%29 Plug in y%5B2%5D=-2,y%5B1%5D=0,x%5B2%5D=5,x%5B1%5D=1 (these are the coordinates of given points)


m=+-2%2F4 Subtract the terms in the numerator -2-0 to get -2. Subtract the terms in the denominator 5-1 to get 4




m=-1%2F2 Reduce



So the slope is

m=-1%2F2





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-0=%28-1%2F2%29%28x-1%29 Plug in m=-1%2F2, x%5B1%5D=1, and y%5B1%5D=0 (these values are given)



y-0=%28-1%2F2%29x%2B%28-1%2F2%29%28-1%29 Distribute -1%2F2


y-0=%28-1%2F2%29x%2B1%2F2 Multiply -1%2F2 and -1 to get 1%2F2

y=%28-1%2F2%29x%2B1%2F2%2B0 Add 0 to both sides to isolate y


y=%28-1%2F2%29x%2B1%2F2 Combine like terms 1%2F2 and 0 to get 1%2F2 (note: if you need help with combining fractions, check out this solver)



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Answer:



So the equation of the line which goes through the points (1,0) and (5,-2) is:y=%28-1%2F2%29x%2B1%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F2 and the y-intercept is b=1%2F2


Notice if we graph the equation y=%28-1%2F2%29x%2B1%2F2 and plot the points (1,0) and (5,-2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F2%29x%2B1%2F2 through the points (1,0) and (5,-2)


Notice how the two points lie on the line. This graphically verifies our answer.