§4 Cartesian Coordinates on a Plane
The coordinate method transforms geometric problems into algebraic ones. By assigning numerical coordinates to points, we can express distances, lines, and curves as equations — then solve them with algebra and interpret the results geometrically.
Learning Objectives
By the end of this chapter you will be able to:
- Use the distance formula and section formula to compute lengths and locate points
- Write and interpret equations of geometric figures, including the circle
- Work with the general equation of a line and derive the distance from a point to a line
- Write line equations in slope-intercept form and through two given points
- Apply the coordinate method to prove geometric theorems and solve locus problems