Chapter 9 Quadratic Relations and Conic Sections - 9.1 Apply the Distance and Midpoint Formulas - 9.1 Exercises - Skill Practice - Page 618: 39

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Find the midpoint of the line segment $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{4+10}{2},\frac{2+8}{2})=(7,5)$ Calculate the slope of AB: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-10}{7-3}=\frac{-5}{4}$ Use point-slope form: $y-5=\frac{-5}{4}(x-7)\\y=-\frac{5}{4}x+\frac{55}{4}$