Final answer:
The centroid of a triangle is found by averaging the x-coordinates and y-coordinates of the vertices of the triangle. Using the formula (x1 + x2 + x3)/3, (y1 + y2 + y3)/3, you can calculate the centroid's coordinates. Apply the formula with the given vertices to obtain the centroid's exact location.
Step-by-step explanation:
Finding the Centroid of a Triangle
To find the centroid of a triangle formed by the intersections of its medians, you need to know the coordinates of the vertices of the triangle. The centroid is the point where the three medians of the triangle intersect, and it is also the balance point of the triangle. The coordinates of the centroid can be found using a simple formula:
(x, y) = ((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)
This formula states that the x-coordinate of the centroid is the average of the x-coordinates of the vertices, and the y-coordinate of the centroid is the average of the y-coordinates of the vertices. Let's go through the steps to calculate the centroid.
1. Identify the coordinates of the vertices of the triangle. Let's say they are A(x_1, y_1), B(x_2, y_2), and C(x_3, y_3).
2. Insert these coordinates into the formula.
3. Calculate the average for the x-coordinates and the y-coordinates separately.
4. The resulting pair of numbers will be the coordinates of the centroid.
For example, if your triangle has vertices at A(2, 4), B(6, 3), and C(1, 9), then by applying the centroid formula:
(x, y) = ((2 + 6 + 1)/3, (4 + 3 + 9)/3)
(x, y) = (9/3, 16/3)
The centroid of the triangle would then be (3, 16/3) or approximately (3, 5.33).