Find the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B
Practice Questions
Q1
Find the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2021)
(4/3, 1, 0)
(2, 1, 0)
(1, 1, 0)
(0, 0, 0)
Questions & Step-by-Step Solutions
Find the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2021)
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 finding 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 A(0, 0, 0), B(4, 0, 0), and C(0, 3, 0), 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 vertices' coordinates.
Coordinate Geometry – Understanding how to work with 3D coordinates and apply formulas to find points in space.
