Coordinate geometry

Place points on a coordinate plane and use distance formulas. The distance between $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$. The midpoint is $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$. The distance from $(x_0,y_0)$ to $Ax+By+C=0$ is $\frac{|A{x}_0+B{y}_0+C|}{\sqrt{A^2+B^2}}$. A perpendicular bisector passes through the midpoint and has slope equal to the negative reciprocal of the segment's slope.