The coordinates of the centroid of a triangle with vertices at (2, 3), (4, 5), a

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Question: The coordinates of the centroid of a triangle with vertices at (2, 3), (4, 5), and (6, 1) are:

Options:

Correct Answer: (4, 3)

Solution:

Centroid = ((2+4+6)/3, (3+5+1)/3) = (4, 3).

The coordinates of the centroid of a triangle with vertices at (2, 3), (4, 5), and (6, 1) are:

The coordinates of the centroid of a triangle with vertices at (2, 3), (4, 5), and (6, 1) are:

Step 1: Identify the coordinates of the triangle's vertices. They are (2, 3), (4, 5), and (6, 1).
Step 2: To find the x-coordinate of the centroid, add the x-coordinates of the vertices: 2 + 4 + 6.
Step 3: Calculate the sum of the x-coordinates: 2 + 4 + 6 = 12.
Step 4: Divide the sum of the x-coordinates by 3 (the number of vertices): 12 / 3 = 4.
Step 5: To find the y-coordinate of the centroid, add the y-coordinates of the vertices: 3 + 5 + 1.
Step 6: Calculate the sum of the y-coordinates: 3 + 5 + 1 = 9.
Step 7: Divide the sum of the y-coordinates by 3: 9 / 3 = 3.
Step 8: Combine the x and y coordinates to get the centroid: (4, 3).

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