The vertices of a triangle are \((-4,\,2)\), \((5,\,-3)\) and \((2,\,7)\). What are the coordinates of its centroid?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \((1,\,2)\)
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: \(-4+5+2=3\)
Sum of the y-coordinates: \(2+(-3)+7=6\)
Centroid \(\displaystyle =\left(\frac{3}{3},\,\frac{6}{3}\right)=(1,\,2)\)
