The vertices of a triangle are \((2,\,-1)\), \((7,\,4)\) and \((-3,\,6)\). What are the coordinates of its centroid?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \((2,\,3)\)
The centroid is the point where the three medians meet. Its coordinates are the averages of the coordinates of the three vertices: \(\displaystyle \left(\frac{x_1+x_2+x_3}{3},\,\frac{y_1+y_2+y_3}{3}\right)\).
Sum of the x-coordinates: \(2+7+(-3)=6\)
Sum of the y-coordinates: \(-1+4+6=9\)
Centroid \(\displaystyle =\left(\frac{6}{3},\,\frac{9}{3}\right)=(2,\,3)\)
