Chapter 9 Quadratic Relations and Conic Sections - 9.1 Apply the Distance and Midpoint Formulas - 9.1 Exercises - Skill Practice - Page 617: 36

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Find the midpoint of the line segment $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{5+10}{2},\frac{10+7}{2})=(\frac{15}{2},\frac{17}{2})$ Calculate the slope of AB: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-10}{10-5}=\frac{-3}{5}$ Find the slope of the perpendicular bisector: $-\frac{1}{m}=\frac{5}{3}$ Use point-slope form: $y-\frac{17}{2}=\frac{5}{3}(x-\frac{15}{2})$