A triangle has vertices with coordinates A(1,2), B(5,2), and C(3,8). What is the y-coordinate of its centroid?
4
Given the three vertices \(A(1,2),\ B(5,2),\ C(3,8)\), we need the y-coordinate of the centroid.
The centroid of a triangle is the average of the coordinates of its three vertices.
Its y-coordinate is given by \(y = \dfrac{y_{1} + y_{2} + y_{3}}{3}\).
Here \(y_{1}=2,\ y_{2}=2,\ y_{3}=8\).
So \(y = \dfrac{2 + 2 + 8}{3}\).
\(y = \dfrac{12}{3} = 4\).
Hence the y-coordinate of the centroid is 4.
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