In △ A B C , , B = ( − 7 , 1 ) , C = ( − 5 , − 5 )Centroid G = ( h , k ) and orthocentre H = ( 3 h , 3 k ) . If A = ( 1 , Y A ) then find Y A

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In   △  A  B  C  , ,   B  =  (  −  7  ,  1  )  ,  C  =  (  −  5  ,  −  5  )Centroid   G  =  (  h  ,  k  ) and orthocentre   H  =  (  3  h  ,  3  k  ) . If   A  =  (  1  ,      Y    A    ) then find       Y    A

knolsaadme · Accepted Answer

Step 1Coordinates of G should be            (                        −          7          −          5          +          1                3            ,                        1          −          5          +                      y            A                          3            )      That gives       h    =    −          11      3        ,          y      A        −    4    =    3    k  and so, we have coordinates of H as       H     as           (      −      11      ,              y        A            −      4      )      Slope of AC,       A    C    ,               m      1        =                            y          A                +        5            6      Slope of BH,      B    H    ,               m      2        =                            y          A                −        5                    −        4            As   B  H  ⊥  A  C  ,         m    1    ⋅      m    2    =  −  1    ⟹        y    A    2    −  25  =  24,       y    A    =  ±  7

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