1) Introduce the students to the rectangular coordinate system by drawing an example on the chalkboard. Label the x-axis, y-axis, origin/point of intersection, and each quadrant, and explain to the students that the rectangular coordinate system is a system that allows for the labeling of points on the plane.
2) Show students several examples of coordinates, explaining that the ordered pair consists of a point on the x-axis and a point on the y-axis. Make sure students see examples within each quadrant so they understand ordered pairs consist of both positive and negative numbers.
3) Introduce students to the distance formula (d=[sqrt]((x1 - x2)[squared] + (y1 - y2)[squared])), explaining that this formula is derived from the Pythagorean Theorem. Demonstrate this derivation on the chalkboard.
4) Show students a few examples on how to calculate the distance formula, using ordered pairs (3,7) and (5,12), (-10, 6) and (8, 15), (-4, -11) and (9, 20), and (16, 4) and (-9, -13).
5) Introduce students to the midpoint formula (mp=(x1 + x2)/2, (y1 + y2)/2), and use several ordered pairs as examples to demonstrate how this formula can be applied.
6) Give students a few minutes to solve the following problem: Find the perimeter of a triangle with vertices at points (2, 2), (6, 5), and (0, 3). After a few minutes, call on a student to provide the answer.
7) Give students a few minutes to solve a second problem: Find the point that is one-quarter the distance from point (10, 14) to (-6, 12). After a few minutes, call on a student to provide the answer.
8) Conclude the class session by asking students if they have any questions. Assign them their homework for the next day.