Determine the coordinates of the centroid of the triangle with vertices A(1, 2,
Practice Questions
Q1
Determine the coordinates of the centroid of the triangle with vertices A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2021)
(4, 5, 6)
(3, 4, 5)
(5, 6, 7)
(6, 7, 8)
Questions & Step-by-Step Solutions
Determine the coordinates of the centroid of the triangle with vertices A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2021)
Step 1: Identify the coordinates of the vertices of the triangle. The vertices are A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9).
Step 2: To find the centroid, we need to calculate the average of the x-coordinates, the average of the y-coordinates, and the average of the z-coordinates of the vertices.
Step 3: Calculate the average of the x-coordinates: (1 + 4 + 7) / 3.
Step 4: Calculate the average of the y-coordinates: (2 + 5 + 8) / 3.
Step 5: Calculate the average of the z-coordinates: (3 + 6 + 9) / 3.
Step 6: Perform the calculations: (1 + 4 + 7) = 12, so 12 / 3 = 4 for the x-coordinate.
Step 7: Perform the calculations: (2 + 5 + 8) = 15, so 15 / 3 = 5 for the y-coordinate.
Step 8: Perform the calculations: (3 + 6 + 9) = 18, so 18 / 3 = 6 for the z-coordinate.
Step 9: Combine the results to get the coordinates of the centroid: G(4, 5, 6).
Centroid of a Triangle – The centroid (or geometric center) of a triangle is the point where the three medians intersect, and its coordinates can be calculated as the average of the coordinates of the vertices.
Coordinate Averaging – Finding the centroid involves averaging the x, y, and z coordinates of the triangle's vertices.
