Question

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⊙ If the three coordinates of a triangle is (3,2) , (4,6) , (7,0) the. what will be the Co ordinate of its centroid ???


⊙ Also , find the area of the triangle ???


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$<b > prabhudutt$


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Answer 1

HEYA MATE, HERE IS UR ANSWER

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$\mathbb {Be\:Brainly}$

Answer 2

$heres \: your \: answer \: \\ \\ here \: the \: given \: cordinates \\ are \: x_{1} = 3 \\ x_{2} = 4\\ x_{3} = 7 \\ y_{1} = 2 \\ y_{2} = 6 \\ y_{3} = 0 \\ \\ so \:let \: the \: centroid \: be \: ( x_{4} \: \: y_{4}) \\ now \: we \: know \: that \: to \: calculate \\ x_{4} \: we \: need \: to \: apply \: the \: \\ following \: formula \: \\ \\ x_{4} = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ = \frac{3 + 4 + 7}{3} \\ = \frac{14}{3} \\ similarly \\ y_{4} = \frac{ y_{1} + y_{2} + y_{3} }{3} \\ = \frac{2 + 6 + 0}{3} \\ = \frac{8}{3} \\ so \: centroid = ( \frac{14}{3} \: \: \: \frac{8}{3} ) \\ \\ for \: area \: \\ = \frac{1}{2}| x_{1}( y_{2} - y_{3}) + x_{2}( y_{3} - y_{1}) + x_{3}( y_{1} - y_{2}) | \\ = \frac{1}{2}|3(6 - 0) + 4(0 - 2) + 7(2 - 6)| \\ = \frac{1}{2} |18 - 8 -28| \\ = \frac{1}{2}|-18| \\ = 9\: {unit}^{2} \\ so \: the \: area \: of \: triangle \: is \: 9 \: {unit}^{2}$