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),
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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) (Show Source): You can put this solution on YOUR website!
Determine the slope of the line that passes through )
and )
:
}{t\ -\ 3t}\ = \frac{-2}{-2t}\ =\ \frac{1}{t})
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:
\ =\ -t(x\ -\ 2t))
Simplify to:
Substitute (5,2) for x and y:
Solve the quadratic for the two possible values for 
John
My calculator said it, I believe it, that settles it
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