SOLUTION: Prove that the equation of the perpendicualr bisector of the points (t, t+1) and (3t, t+3) is y + tx = 2t^2 + t + 2. If this perpendicular bisector passes through the point (5,2),

Algebra ->  Coordinate-system -> SOLUTION: Prove that the equation of the perpendicualr bisector of the points (t, t+1) and (3t, t+3) is y + tx = 2t^2 + t + 2. If this perpendicular bisector passes through the point (5,2),      Log On


   

Question 391317: Prove that the equation of the perpendicualr bisector of the points (t, t+1) and (3t, t+3) is y + tx = 2t^2 + t + 2. If this perpendicular bisector passes through the point (5,2), calculate all the possible values of t.
Answer by solver91311(24713) About Me  (Show Source):
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Determine the slope of the line that passes through and :



The negative reciprocal of the slope is the slope of the perpendicular, so:



Determine the midpoint of the given segment:

and



Write the desired equation using the point-slope form:



Simplify to:



Substitute (5,2) for x and y:





Solve the quadratic for the two possible values for

John

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