Final answer:
The centroid of a triangle with vertices at (1, 10), (-5, 2), and (7, 3) is found to be at the coordinates (1, 5).
Step-by-step explanation:
The centroid of a triangle is found by taking the average of the x-coordinates and the average of the y-coordinates of the three vertices. Let's find the centroid of the triangle with vertices at (1, 10), (-5, 2), and (7, 3). To find the x-coordinate of the centroid, add up the x-coordinates of the vertices and divide by 3: (1 - 5 + 7) / 3 = 3 / 3 = 1. To find the y-coordinate of the centroid, add up the y-coordinates of the vertices and divide by 3: (10 + 2 + 3) / 3 = 15 / 3 = 5. Therefore, the centroid has coordinates (1, 5).