Question

If (-2,1) is the centroid of triangle having its vertices at (x,2),(10,-2) ,(-8,y) then x, y satisfy the relation

Answer 1

Answer:

X,Y satisfies the relation for the given relation

Answer 2

$Given \: G(-2,1) \: is \:the \: centroid \: of$

$triangle \: having \: it's \: Vertices \: at \:(x,2)$

$(10,-2) \: and \: (-8,y)$

$We \: know \: that,$

$\blue{Centroid \: of \: a\: triangle \: whose}$

$\blue{Vertices \: are \: (x_{1},y_{1}) , \: (x_{2},y_{2})}$

$\blue {and \: (x_{3},y_{3}) \: is} \: \pink {\Big( \frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\Big) }$

$\Big( \frac{x+10-8}{3}, \frac{2-2+y}{3}\Big) = (-2,1)$

$\implies \Big( \frac{x+2}{3} , \frac{y}{3}\Big) = (-2,1)$

$\implies \frac{x+2}{3} = -2 \:and \: \frac{y}{3} = 1$

$\implies x + 2 = -6 \: and \: y = 3$

$\implies x = -6 -2 \: and \: y = 3$

$\implies x = -8 \: and \: y = 3$

Therefore.,

$\red{ ( x ,y ) } \green { = ( -8, 3) }$

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