The student understands that coordinate systems provide a convenient and efficient way of representing geometric figures and uses them accordingly. The student develops and uses formulas including distance and midpoint. Clarifying Activity Students are given several different triangles with the coordinates of the vertices. Clarifying Activity Students select two points on the coordinate plane. Students locate a third point in order to form a right triangle in which the first two points selected are the endpoints of the hypotenuse of the triangle.
Students repeat the process for another pair of points.
Students look for patterns in their process to determine a method for using the coordinates of two points to determine the distance between the points and thus develop the distance formula. A similar activity can be used to develop the midpoint formula.