Final answer:
To find the centroid of a triangle, corners (vertices) must be determined first, and then the formula is used which averages the x-coordinates and y-coordinates of the vertices.
Step-by-step explanation:
To find the centroid of a triangle bounded by the given lines, we first need to determine the vertices of this triangle by finding the points of intersection of the lines. The equations provided correspond to lines that form the sides of the triangle. By solving the equations pairwise, we obtain the coordinates of the vertices.
Let's find the intersection of the first two lines by solving the system of equations formed by 4x - y + 18 = 0 and 3x - 13y - 11 = 0.
We repeat the process for the other pairs to find the remaining vertices.
Once we have the vertices, we use the formula for the centroid which is the average of the x-coordinates and the y-coordinates of the vertices (x1 + x2 + x3)/3, (y1 + y2 + y3)/3. This will give us the coordinates of the centroid of the triangle.
The centroid is the point where the medians of the triangle intersect. It is also the center of mass of a triangle if it's made from a uniform material.