Determine the coordinates of the centroid of the triangle with vertices A(0, 0,
Practice Questions
Q1
Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2023)
(1, 1, 0)
(2, 1, 0)
(4/3, 1, 0)
(0, 1, 0)
Questions & Step-by-Step Solutions
Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2023)
Step 1: Identify the coordinates of the vertices of the triangle. The vertices are A(0, 0, 0), B(4, 0, 0), and C(0, 3, 0).
Step 2: Write down the formula for the centroid (G) of a triangle with vertices (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). The formula is G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3, (z1 + z2 + z3)/3).
Step 3: Substitute the coordinates of the vertices into the formula. For our triangle, we have: G = ((0 + 4 + 0)/3, (0 + 0 + 3)/3, (0 + 0 + 0)/3).
Step 4: Calculate the x-coordinate of the centroid: (0 + 4 + 0)/3 = 4/3.
Step 5: Calculate the y-coordinate of the centroid: (0 + 0 + 3)/3 = 1.
Step 6: Calculate the z-coordinate of the centroid: (0 + 0 + 0)/3 = 0.
Step 7: Combine the calculated coordinates to find the centroid: G = (4/3, 1, 0).
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 Geometry – Understanding how to work with 3D coordinates and apply formulas to find points in space.
