Overview

Coordinate geometry translates geometry into algebra. Use slopes for collinearity and the distance formula for lengths.

Key Ideas

• Distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
• Midpoint formula: $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.
• Parallel lines have equal slopes, perpendicular lines have slopes that multiply to $-1$.

Worked Example

Find the equation of the line through $(2,3)$ and $(6,11)$.

Slope is $\frac{11-3}{6-2}=2$, so the line is $y-3=2(x-2)$ or $y=2x-1$.

Practice Problems