What is the coordinates of the centroid of the triangle with vertices (0, 0), (6

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Question: What is the coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (3, 6)? (2022)

Options:

Correct Answer: (3, 2)

Solution:

Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).

What is the coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (3, 6)? (2022)

What is the coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (3, 6)? (2022)

Step 1: Identify the coordinates of the vertices of the triangle. The vertices are (0, 0), (6, 0), and (3, 6).
Step 2: To find the x-coordinate of the centroid, add the x-coordinates of all three vertices: 0 + 6 + 3.
Step 3: Calculate the sum from Step 2: 0 + 6 + 3 = 9.
Step 4: Divide the sum from Step 3 by 3 (the number of vertices): 9 / 3 = 3. This is the x-coordinate of the centroid.
Step 5: To find the y-coordinate of the centroid, add the y-coordinates of all three vertices: 0 + 0 + 6.
Step 6: Calculate the sum from Step 5: 0 + 0 + 6 = 6.
Step 7: Divide the sum from Step 6 by 3: 6 / 3 = 2. This is the y-coordinate of the centroid.
Step 8: Combine the x and y coordinates to get the centroid: (3, 2).

Centroid of a Triangle – The centroid is the point where the three medians of the triangle intersect, and its coordinates can be calculated as the average of the vertices' coordinates.