A ( 1 , 4 ) , B ( 2 , 3 ) are the vertices of △ A B C .Centroid of the triangle lies on the locus 3 x − 9 y + 13 = 0If the equation of the locus of the third vertex C is x − b y − c = 0 then find ( b + c )

Question

A  (  1  ,  4  )  ,   B  (  2  ,  3  ) are the vertices of   △  A  B  C .Centroid of the triangle lies on the locus  3  x  −  9  y  +  13  =  0If the equation of the locus of the third vertex C is   x  −  b  y  −  c  =  0 then find   (  b  +  c  )

Alisa Gilmore · Accepted Answer

Step 1The question setter is telling you that as C moves along the line   x  −  b  y  −  c  =  0 then G moves along the line   3  x  −  9  y  +  13  =  0As you have realised, if you let C be (h,k) then G is            (                          h        +        3            3        ,                    k        +        7            3                  )      When you now substitute the coordinates of G into the equation   3  x  −  9  y  +  13  =  0 you will obtain a linear equation between h and k, which is exactly what the equation   x  −  b  y  −  c  =  0 is.

A ( 1 , 4 ) , B ( 2 , 3 ) are the vertices of <mi m

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