find the coordinates of the centroid of a triangular metal part with vertices at A(12,18) B(18,6), and C(3,12)
To find the coordinates of the centroid of a triangular metal part, you can use the following steps:
1. Identify the coordinates of the three vertices of the triangle: A(12, 18), B(18, 6), and C(3, 12).
2. Find the average of the x-coordinates of the three vertices. To do this, add up the x-coordinates (12 + 18 + 3) and divide the sum by 3, the number of vertices. (12 + 18 + 3) / 3 = 33 / 3 = 11.
So, the x-coordinate of the centroid is 11.
3. Find the average of the y-coordinates of the three vertices. Add up the y-coordinates (18 + 6 + 12) and divide the sum by 3: (18 + 6 + 12) / 3 = 36 / 3 = 12.
Thus, the y-coordinate of the centroid is 12.
4. Therefore, the coordinates of the centroid are (11, 12).
You can also use the equation for the centroid of a triangle, which states that the coordinates of the centroid are the average of the coordinates of the vertices. This equation can be expressed as follows:
Centroid = ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3).
By substituting the given coordinates into this equation, you should get the same result: (11, 12).