The coordinates of the centroid of a triangle with vertices at (1, 2), (3, 4), a

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

Options:

Correct Answer: (3, 4)

Solution:

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

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

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

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

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 triangle's vertices.