$\"\"$

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The given vertices of the triangle are $\"\"$ .

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Find an equation of median from Vertex F to midpoint of $\"\"$ .

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The midpoint of $\"\"$ .

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The endpoints of the median are $\"\"$ .

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The slope of the median is $\"\"$

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$\"\"$ (Point-slope form)

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$\"\"$ (Substitute $\"\"$ , $\"\"$ )

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$\"\"$ (Distributive property)

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$\"\"$ (Add 2 to each side)

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$\"\"$ (Add 4x to each side) $\"\"$

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Find an equation of median from Vertex E to midpoint of $\"\"$ .

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The midpoint of $\"\"$ .

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The endpoints of the median are $\"\"$ .

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The slope of the median is $\"\"$

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$\"\"$ (Point-slope form)

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$\"\"$ (Substitute $\"\"$ , $\"\"$ )

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$\"\"$ (Multiply each side by 4)

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$\"\"$ (Distributive property)

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$\"\"$ (Add 12 to each side)

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$\"\"$ (Add x to each side) $\"\"$

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Solve a system of equations to find the point of intersection of the medians.

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$\"\"$

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So, $\"\"$ . $\"\"$

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Use y value to determine the x-coordinate.

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$\"\"$ (Write the equation)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify)

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$\"\"$ (Subtract $\"\"$ from each side)

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So, $\"\"$

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$\"\"$

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The coordinates of centroid are $\"\"$ .