Question

The coordinates of the vertices of a triangle are \( (2, 4) \), \( (0, 6) \) and \( (4, -1) \). Then the coordinates of the centroid of the triangle are:

• A. \( (2, 3) \)
• B. \( (3, 2) \)
• C. \( (3, 3) \)
• D. \( (2, 2) \)

Hint:

Centroid is the average of the three vertices’ coordinates: add the \(x\)'s and \(y\)'s separately and divide each by \(3\).

Answer 1

The Correct Option is A

Step 1: Recall centroid formula.
For triangle with vertices \( (x_1,y_1), (x_2,y_2), (x_3,y_3) \), centroid \( G \) is
\[ G\left(\frac{x_1+x_2+x_3}{3},\; \frac{y_1+y_2+y_3}{3}\right). \]
Step 2: Substitute the given coordinates.
\[ G\left(\frac{2+0+4}{3},\; \frac{4+6+(-1)}{3}\right) = \left(\frac{6}{3},\; \frac{9}{3}\right) = (2, 3). \]
Step 3: Conclude.
Thus, the centroid of the triangle is \( (2, 3) \).