Chapter 9 Quadratic Relations and Conic Sections - 9.1 Apply the Distance and Midpoint Formulas - 9.1 Exercises - Skill Practice - Page 617: 34

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Find the midpoint of the line segment $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{1+6}{2},\frac{4-6}{2})=(\frac{7}{2},-1)$ Calculate the slope of AB: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{-6-4}{6-1}=-2$ Find the slope of the perpendicular bisector: $-\frac{1}{m}=\frac{1}{2}$ Use point-slope form: $y+1=\frac{1}{2}(x-\frac{7}{2})$