Chapter 1 - Tools of Geometry - 1-7 Midpoint and Distance in the Coordinate Plane - Practice and Problem-Solving Exercises - Page 55: 49

a) $d=10.8$ b) $M(3, -4)$

Given $A(-2,-2)$ and $B(8,-6)$ a) Use the distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ $d=\sqrt{(8-(-2))^2+(-6-(-2))^2}$ $d=\sqrt{(10)^2+(-4)^2}$ $d=\sqrt{100+16}$ $d=\sqrt{116}$ $d\approx10.8$ b) Use the midpoint formula: $M_x=\frac{x_1+x_2}{2}=\frac{-2+8}{2}=\frac{6}{2}=3$ $M_y=\frac{y_1+y_2}{2}=\frac{-2+(-6)}{2}=\frac{-8}{2}=-4$