Question

What is the centroid of the triangle whose vertices are (6, 2), (2, 3) and (4, -8)?

• A. $\left( \frac{13}{3}, -1 \right)$
• B. $\left( -\frac{2}{3}, \frac{5}{3} \right)$
• C. $(4, -1)$
• D. $(2, -1)$

Hint:

Centroid is simply the average of coordinates. Add all x-values and divide by 3, and do the same for y-values.

Answer 1

The Correct Option is C

Concept: The centroid of a triangle is the arithmetic mean of the coordinates of its vertices. It is the point where all three medians intersect and acts as the geometric center of the triangle. For vertices \((x_1,y_1), (x_2,y_2), (x_3,y_3)\), centroid is: \[ G = \left( \frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3} \right) \]

Step 1: Identify coordinates.
• \( (x_1,y_1) = (6,2) \)
• \( (x_2,y_2) = (2,3) \)
• \( (x_3,y_3) = (4,-8) \)

Step 2: Compute x-coordinate. \[ x_G = \frac{6+2+4}{3} = \frac{12}{3} = 4 \]

Step 3: Compute y-coordinate. \[ y_G = \frac{2+3-8}{3} = \frac{-3}{3} = -1 \] Final Answer: \[ G = (4,-1) \]