Find the co-ordinates of centroid whose triangle vertices are (0, 6), (8, 12) and (8, 0)

(\frac{16}{3}, 6)

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(- \frac{16}{3}, 6)

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(\frac{16}{3}, - 6)

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none of the above

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Solution

The correct option is A $(\frac{16}{3}, 6)$
We know that the co-ordinates of the centroid of a triangle whose angular points are $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3}) a r e (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$
So the co-ordinates of the centroid of a triangle whose vertices are (0, 6), (8, 12) and (0, 8) are $(\frac{0 + 8 + 8}{3}, \frac{6 + 12 + 0}{3}) o r (\frac{16}{3}, 6)$

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Find the co-ordinates of centroid whose triangle vertices are (0, 6), (8, 12) and (8, 0)

The correct option is A (163,6)We know that the co-ordinates of the centroid of a triangle whose angular points are (x1,y1),(x2,y2),(x3,y3)are(x1+x2+x33,y1+y2+y33)So the co-ordinates of the centroid of a triangle whose vertices are (0, 6), (8, 12) and (0, 8) are (0+8+83,6+12+03)or(163,6)