1. **State the problem:** Find the equation of one median of the triangle with vertices A(2,3), B(8,1), and C(5,7), and find the point of concurrency (centroid) of the medians. 2. **Recall the definition of a median:** A median connects a vertex to the midpoint of the opposite side. 3. **Find the midpoint of side BC:** $$\text{Midpoint } M = \left(\frac{8+5}{2}, \frac{1+7}{2}\right) = (\frac{13}{2}, 4) = (6.5, 4)$$ 4. **Find the slope of median AM:** $$m = \frac{4 - 3}{6.5 - 2} = \frac{1}{4.5} = \frac{2}{9}$$ 5. **Write the equation of the median AM in point-slope form:** $$y - 3 = \frac{2}{9}(x - 2)$$ 6. **Convert to slope-intercept form:** $$y = \frac{2}{9}x - \frac{4}{9} + 3 = \frac{2}{9}x + \frac{23}{9}$$ 7. **Find the centroid (point of concurrency):** The centroid is the average of the vertices' coordinates: $$x_c = \frac{2 + 8 + 5}{3} = \frac{15}{3} = 5$$ $$y_c = \frac{3 + 1 + 7}{3} = \frac{11}{3} \approx 3.67$$ **Final answers:** - Equation of median from A: $$y = \frac{2}{9}x + \frac{23}{9}$$ - Centroid coordinates: $$(5, \frac{11}{3})$$