Question

The vertices of a triangle are \( (7, 5) \), \( (5, 7) \), and \( (-3, 3) \). Then the centroid of the triangle will be:

• A. \( (3, 5) \)
• B. \( (-3, 5) \)
• C. \( (3, -5) \)
• D. \( (5, 3) \)

Hint:

The centroid of a triangle is the average of the coordinates of its three vertices.

Answer 1

The Correct Option is A

The centroid of a triangle is the point where the three medians of the triangle intersect. The coordinates of the centroid \( G(x, y) \) can be found using the formula: \[ x = \frac{x_1 + x_2 + x_3}{3}, \quad y = \frac{y_1 + y_2 + y_3}{3} \] where \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are the coordinates of the vertices of the triangle. Given vertices are \( (7, 5) \), \( (5, 7) \), and \( (-3, -3) \). Step 1: Calculate the x-coordinate of the centroid: \[ x = \frac{7 + 5 + (-3)}{3} = \frac{9}{3} = 3 \] Step 2: Calculate the y-coordinate of the centroid: \[ y = \frac{5 + 7 + 3}{3} = \frac{15}{3} = 5 \] Thus, the centroid is \( (3, 5) \).