SOLUTION: Analytic Geometry For JKL, find an equation for a) the median from vertex J b) the median from vertex K c) the right bisector of side JL. J(1,4), K(-3,-1), and L(3,-4).

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Question 1142125: Analytic Geometry For JKL, find an equation for a) the median from vertex J b) the median from vertex K c) the right bisector of side JL. J(1,4), K(-3,-1), and L(3,-4).
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
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(a)  The median from vertex J goes through the point J= (1,4)  and the midpoint of KL, which (midpoint) is (0,-2.5).


     So, the slope of this median is  m =  =  = 6.5.


     Therefore, the equation of this median from vertex J is


         y-4 = 6.5*(x-1).


     You can transform this equation to any equivalent form you want / (you need).




(b)  To solve (b),  do it similarly, having my solution to (a) as a TEMPLATE before your eyes.




(c)  The segment JL has the slope


     m =  =  = -4.


    Hence, the perpendicular line to segment JL has the slope of 0.25.


    The midpoint of the segment JL is the point (2,0).


    Therefore, the equation of the right bisector to side JL is


        y = 0.25*(x-2).


     You can transform this equation to any equivalent form you want / (you need).

Answered, explained and solved.


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    - Equation for a straight line having a given slope and passing through a given point
    - Solving problems related to the slope of a straight line
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    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point
that are closely related to your problem.

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