The question is as follows:Let K ( 5 , 12 ), L ( 14 , 0 ) and M ( 0 , 0 ). The line x + 2 y = 14 bisects angle M L K. Find equations for the bisectors of the angles K M L and M K L.Any help will be truly appreciated!

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The question is as follows:Let   K  (  5  ,  12  ),   L  (  14  ,  0  ) and   M  (  0  ,  0  ). The line   x  +  2  y  =  14 bisects angle   M  L  K. Find equations for the bisectors of the angles   K  M  L and   M  K  L.Any help will be truly appreciated!

Elijah Benjamin · Accepted Answer

Let   K  D be bisector of   Δ  K  L  M.Thus, since            L      D              D      M        =            K      L              K      M        =                    9        2            +              12        2                            5        2            +              12        2              =      15    13    ,we obtain  D      (                  13        ⋅        14        +        0                    15        +        13              ,    0    )  or  D  (  6.5  ,  0  )  .Thus,      m          K      D        =            12      −      0              5      −      6.5        =  −  8and for the equation of   K  D we obtain:  y  −  12  =  −  8  (  x  −  5  )or  y  =  −  8  x  +  52.Now,   y  =  −  8  x  +  52 and   x  +  2  y  =  14 intersect in the point   I  (  6  ,  4  ).Thus, for the equation of the third bisector we obtain:  y  −  0  =            4      −      0              6      −      0        (  x  −  0  )or  y  =      2    3    x  .Done!

Kyle Sutton · Accepted Answer

First, let&#039;s find equations for line   M  K which is easy:   y  =      12    5    x. Now the points that belong to bisector are equidistant from   M  K and   M  L (which is axis x). To find the slope we need to find tangent of one half of   ∠  K  M  L. We can use trigonometric identity for that:   t  a  n            x      2        =                    1        −        c        o        s        x                    1        +        c        o        s        x            . Thus, the equation for   ∠  K  L  M bisector is   y  =      2    3    x. Now we need to find equation for line   K  L which is   y  =  −      4    3    x  +      56    3  . The equation for bisector of   ∠  K  L  M will be            0      =                        |          −                      4            3                    x          −          y          +                      56            3                    |                          1          +                      16            9

The question is as follows: Let K ( 5 , 12 ) , L ( 14 , 0 )

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