Determine the coordinates of the centroid of the triangle with vertices A(0, 0,

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Question: Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(6, 0, 0), and C(0, 8, 0). (2023)

Options:

Correct Answer: (2, 2, 0)

Exam Year: 2023

Solution:

Centroid = ((0+6+0)/3, (0+0+8)/3, (0+0+0)/3) = (2, 2.67, 0).

Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(6, 0, 0), and C(0, 8, 0). (2023)

Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(6, 0, 0), and C(0, 8, 0). (2023)

Step 1: Identify the coordinates of the vertices of the triangle. The vertices are A(0, 0, 0), B(6, 0, 0), and C(0, 8, 0).
Step 2: Write down the formula for the centroid of a triangle. The formula is: Centroid = ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3, (z1 + z2 + z3) / 3).
Step 3: Substitute the coordinates of the vertices into the formula. For A(0, 0, 0), B(6, 0, 0), and C(0, 8, 0), we have: Centroid = ((0 + 6 + 0) / 3, (0 + 0 + 8) / 3, (0 + 0 + 0) / 3).
Step 4: Calculate the x-coordinate of the centroid: (0 + 6 + 0) / 3 = 6 / 3 = 2.
Step 5: Calculate the y-coordinate of the centroid: (0 + 0 + 8) / 3 = 8 / 3 = 2.67.
Step 6: Calculate the z-coordinate of the centroid: (0 + 0 + 0) / 3 = 0 / 3 = 0.
Step 7: Combine the calculated coordinates to find the centroid: The centroid is (2, 2.67, 0).

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 vertices' coordinates.
Coordinate Geometry – Understanding how to work with 3D coordinates and apply formulas to find points in space.