The triangle with vertices located at A(1 , 7), B(4 , 2), and C(7 , 7) has its centroid located at (4 , 16/3).
The centroid of a triangle is the point inside the triangle where the three medians intersect. The median of a triangle is the line the connects the midpoint of a side and the opposite vertex.
To get the centroid of a triangle, use the formula given by:
C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]
where C is the centroid of the triangle located at (x , y)
x1, x2, and x3 are the x-coordinate of the vertices of the triangle
y1, y2, and y3 are the y-coordinate of the vertices of the triangle
Let Point 1(x1 , y1) = A(1 , 7)
Point 2(x2 , y2) = B(4 , 2)
Point 3(x3 , y3) = C(7 , 7)
Plug in the values in the formula.
C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]
C(x ,y) = [(1 +4 + 7)/3 , (7 + 2 + 7)/3]
C(x ,y) = (12/3 , 16/3)
C(x ,y) = (4 , 16/3)
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