Question

The vertices of a triangle are A(-5, 3), B(P,-1) and C(6.9) Find the values of P and q. If the centroid of the AABC is the point

(1, -1).​

Answer 1

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Q1) The vertices of a triangle are A(-5,-3) ,B(P,-1) and C(6,9).Find the value of P and Q, If the centroid of the ABC is the point (-1,1) .

$\LARGE {\underline {\red {\sf{Required \: Answer :}}}}$

$\: \: \bigstar \bf{by \: using \:centroid\: method}$

$\bullet\displaystyle\bf{x=\dfrac{x_1+x_2+x_3}{3} \: and \: y=\dfrac{y_1+y_2+y_3}{3}}$

$\boxed{\sf{Given\: values }}$

$\: \bullet \bf{x = - 1 \: and \: y = 1}$

$\bullet \bf{x_1=-5 , x_2=P ,x_3=6}$

$\bullet \bf{y_1=-3,y_2=-1 and y_3=9}$

$\\ \implies \bf{substitute \: the \: given \: values}$

$\: \implies \displaystyle \sf{x = \frac{x1 + x2 + x3}{3} }$

$\: \implies \displaystyle \sf{ - 1 = \frac{5 + p + 6}{3} }$

$\: \: \implies \displaystyle \sf{ - 3 = 11 + p}$

$\: \implies \displaystyle \sf{ - 3 - 11 - p = 0}$

$\: \implies \displaystyle \sf{p = 14}$

$\: \bigstar \underline{\boxed{ \bf{the \: value \: of \: p = 14}}}$