Understands and applies coordinates
Coordinates are used to specify location. For example, the coordinates (2, 3) specify the location of a point in the plane that is 2 units to the right of the origin and 3units up. Rectangular coordinates (also called Cartesian coordinates) are coordinates calculated with respect to horizontal and vertical lines, such as the x-axis and y-axis.
Rectangular coordinates are the focus of the study of coordinate geometry in the core curriculum. However, students should recognize that the location of a point can be, and often is, also described using angle and distance. The study of coordinate geometry includes investigating conjectures, modeling, and solving problems. By using inductive and deductive reasoning with coordinates, properties of geometric objects can be conjectured and verified.
Coordinates can be used to describe points, lines, and other two- and three-dimensional figures. Transformations of these objects can be described using coordinate rules. Analysis of the relationships of these geometric objects will include the use of formulas for distance, midpoint, and slope (parallel and perpendicular), and the Pythagorean Theorem. Students should find and analyze equations that represent lines, circles and parabolas. (Students should be introduced to the other conic sections-ellipses and hyperbolas). In three dimensions, students should be able to plot points using rectangular coordinates, and also understand and use longitude and latitude on the surface of the Earth.