Question

When the three medians of the triangle are drawn, they meet at a single point. What is the point of the centroid?
(3,5)
(3,14/3)
(10/3,14/3)
(3,6)

Answer 1

The point of concurrency of the medians of a triangle is called the centroid. To find the coordinates of the centroid, we take the average of the coordinates of the three vertices.

Let's consider the given coordinates for the vertices of the triangle: (3,5), (3,14/3), and (10/3,14/3).

The x-coordinate of the centroid is the average of the x-coordinates of the vertices:
(x1 + x2 + x3) / 3 = (3 + 3 + 10/3) / 3 = (9 + 10)/3 / 3 = 19/3 / 3 = 19/9 = 10/3

The y-coordinate of the centroid is the average of the y-coordinates of the vertices:
(y1 + y2 + y3) / 3 = (5 + 14/3 + 14/3) / 3 = (15/3 + 14/3 + 14/3) / 3 = 43/3 / 3 = 43/9 = 14/3

Therefore, the coordinates of the centroid are (10/3, 14/3).

The correct answer is (10/3, 14/3).