1. Midpoint formula: $$M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$ A. Find the midpoint: 1. For P(-1,-6) and R(-6,5): $$M=\left(\frac{-1-6}{2},\frac{-6+5}{2}\right)=\left(\frac{-7}{2},\frac{-1}{2}\right)=\left(-3.5,-0.5\right)$$ 2. For W(-1.2,1.0) and A(5.2,-5.3): $$M=\left(\frac{-1.2+5.2}{2},\frac{1.0-5.3}{2}\right)=\left(\frac{4.0}{2},\frac{-4.3}{2}\right)=\left(2.0,-2.15\right)$$ 3. For C(2,-1) and T(-6,0): $$M=\left(\frac{2-6}{2},\frac{-1+0}{2}\right)=\left(\frac{-4}{2},\frac{-1}{2}\right)=\left(-2,-0.5\right)$$ B. Find the other endpoint using midpoint formula rearranged: $$x_2=2x_m - x_1,\quad y_2=2y_m - y_1$$ 1. Endpoint (2,5), Midpoint (5,1): $$x_2=2(5)-2=10-2=8$$ $$y_2=2(1)-5=2-5=-3$$ Other endpoint: (8,-3) 2. Endpoint (-1,9), Midpoint (-9,-10): $$x_2=2(-9)-(-1)=-18+1=-17$$ $$y_2=2(-10)-9=-20-9=-29$$ Other endpoint: (-17,-29)