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  • Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of D ABC. If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are the vertices of D ABC, find the coordinates of the centroid of the triangle.

7.(v)   Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of \triangle ABC. If A(x_1, y_1), B(x_2, y_2)\ and\ C(x_3, y_3)  are  the vertices   of  \triangle ABC, find the coordinates of the centroid of the triangle.

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best_answer

From the figure,

Let the median be AD which divides the side BC into two equal parts.

Therefore, D is the mid-point of side BC.

Coordinates of D:

= \left ( \frac{x_{2}+x_{3}}{2}, \frac{y_{2}+y_{3}}{2} \right )

Let the centroid of this triangle be O.

Then, point O divides the side AD in a ratio 2:1.

Coordinates of O:

= \left ( \frac{2\times\frac{x_{2}+x_{3}}{2}+1\times x_{1}}{2+1}, \frac{2\times\frac{y_{2}+y_{3}}{2}+1\times y_{1} }{2+1} \right )

= \left ( \frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3} \right )

 

Posted by

Divya Prakash Singh

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