Find the coordinates of the centroid of the triangle with vertices at (0, 0), (6
Practice Questions
Q1
Find the coordinates of the centroid of the triangle with vertices at (0, 0), (6, 0), and (3, 6).
(3, 2)
(3, 3)
(2, 3)
(0, 0)
Questions & Step-by-Step Solutions
Find the coordinates of the centroid of the triangle with vertices at (0, 0), (6, 0), and (3, 6).
Correct Answer: (3, 2)
Step 1: Identify the coordinates of the vertices of the triangle. The vertices are (0, 0), (6, 0), and (3, 6).
Step 2: Label the coordinates. Let (x1, y1) = (0, 0), (x2, y2) = (6, 0), and (x3, y3) = (3, 6).
Step 3: Use the formula for the centroid of a triangle: Centroid = ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3).
Step 4: Calculate the x-coordinate of the centroid: (0 + 6 + 3) / 3 = 9 / 3 = 3.
Step 5: Calculate the y-coordinate of the centroid: (0 + 0 + 6) / 3 = 6 / 3 = 2.
Step 6: Combine the x and y coordinates to find the centroid: The centroid is (3, 2).
Centroid of a Triangle – The centroid is the point where the three medians of the triangle intersect, and its coordinates can be calculated as the average of the vertices' coordinates.
