Find the coordinates of the centroid of triangle ABC with vertices A(1, -5), B(-4, 0), and C(3, -4). What are the centroid coordinates (x, y)?

Introduction / Context:
This question checks the centroid formula in coordinate geometry. The centroid is the intersection point of the medians and is also the “average” of the vertex coordinates in a triangle.

Given Data / Assumptions:

• A(1, -5)
• B(-4, 0)
• C(3, -4)

Concept / Approach:
The centroid G(xg, yg) of triangle with vertices (x1, y1), (x2, y2), (x3, y3) is: xg = (x1 + x2 + x3)/3 yg = (y1 + y2 + y3)/3 This works because each median divides the triangle into equal areas, and the centroid balances the triangle.

Step-by-Step Solution:

Verification / Alternative check:
You can also find the midpoint of BC and check that the median from A passes through (0, -3). Since centroid lies 2/3 of the way from a vertex to the opposite midpoint, the computed average point is consistent with triangle median properties.

Why Other Options Are Wrong:

Common Pitfalls:
Dividing by 2 instead of 3 (confusing with midpoint), or sign errors while adding negative coordinates.

Final Answer:
(0, -3)