The co-ordinates of the centroid of a triangle PQR are (2, -5). If Q = (-6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.

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Solution

Let G be the centroid of PQR whose coordinates are (2, -5) and let (x,y) be the coordinates of vertex P.

$C o minus o r d i n a t e s space o f space G space a r e G left parenthesis 2 comma negative 5 right parenthesis equals G open parentheses fraction numerator x minus 6 plus 11 over denominator 3 end fraction comma fraction numerator y plus 5 plus 8 over denominator 3 end fraction close parentheses 2 equals fraction numerator x plus 5 over denominator 3 end fraction comma space space space minus 5 equals fraction numerator y plus 13 over denominator 3 end fraction 6 equals x plus 5 space space space comma negative 15 equals y plus 13 x equals 1 space space space space space space space space space comma y equals negative 28 C o minus o r d i n a t e s space o f space v e r t e x space p space a r e space left parenthesis 1 comma negative 28 right parenthesis$

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