Students describe rectangles (with edges parallel to the axes) and triangles in the coordinate plane by means of inequalities. For example, the rectangle in the coordinate plane with lower left vertex (1,2) and upper right vertex (10,15) is {(x,y) l 1 < x < 10 & 2 < y < 15} , the triangle with vertices at (0,0), (1,3), and (2,1) is {(x,y) l x/2 < y < 3x & y < -2x + 5}.

Given two points in the coordinate plane and a rectangular or triangular region, students determine whether the line through those points meets the region, and if it does, they describe the intersections as a segment and name the coordinates of the endpoints.

Given a segment in the coordinate plane, students find the segments obtained by rotating the given segment by 90° counterclockwise and clockwise about one endpoint.

Students explain the connection between the Pythagorean Theorem and the criterion for perpendicularity.

Students recognize parallel and perpendicular lines from slope.
Students create equations for lines satisfying criteria of the kind: “Contains a given point and is parallel/perpendicular to a given line.”

The challenge of programming robot motion along segments parallel or perpendicular to a given segment leads to an analysis of slopes of parallel and perpendicular lines. Students write equations for parallel, perpendicular, and normal lines. Additionally, students will and study the proportionality of segments formed by diagonals of polygons.

Students find the perimeter of a quadrilateral in the coordinate plane given its vertices and edges.
Students find the area of a quadrilateral in the coordinate plane given its vertices and edges by employing Green’s theorem.

Students find the perimeter of a triangle or quadrilateral in the coordinate plane given a description by inequalities.
Students find the area of a triangle or quadrilateral in the coordinate plane given a description by inequalities by employing Green’s theorem.

Students find the perimeter of a triangle in the coordinate plane using the distance formula.
Students state and apply the formula for area of a triangle with vertices (0,0),(x1, y1), and (x2 , y2).

Students find midpoints of segments and points that divide segments into 3, 4, or more proportional, equal parts.

Using coordinates, students prove that the intersection of the medians of a triangle meet at a point that is two-thirds of the way along each median from the intersected vertex.
Using coordinates, students prove the diagonals of a parallelogram bisect one another and meet at the intersection of the segments joining the midpoints of opposite sides.

Students name several points on a line given by a parametric equation and provide the point-slope equation for a line given by a parametric equation.
Students determine whether lines given parametrically are parallel or perpendicular.

Given a circle, students find the equations of two lines tangent to the circle with specified slopes.
Given a circle and a point outside the circle, students find the equation of the line tangent to the circle from that point.

This stand-alone module examines the history, applications, and various proofs of the Pythagorean Theorem. The module also includes student activities and exercise problems. The module assumes the reader has a basic geometry background.

The purpose of this task is to develop the distance formula, based upon students’ understanding of the Pythagorean theorem. In the task, students are asked to calculate distances between points using triangles, and then to formalize the process to the distance formula. At the end of the task, students will use the distance formula to find the perimeter of a hexagon.

Students are given 4-5 coordinate points, that will represent the sheep.  First, they are tasked with creating a fence around the sheep. The students will use the endpoints of each piece of fence to compute the slope, y-intercept, domain and equation of the line. They will then code the rover to draw their lines. Finally, the students can calculate the area/perimeter of their fence and calculate the cost to build the fence. The students will then be challenged to minimize the area, perimeter and cost of building their corral, recalculate the equations of their lines, stating their new slope, y-intercept, and domain.

Advanced lesson involving using geometric figures in the coordinate plane to find slopes of lines, distances between two points, and the midpoints between two points. From that point, students can classify polygons based on their definition.

Distance Formula in the Coordinate PlaneIn this lesson, students will be able to take notes on finding perimeter in the coordinate plane by a Prezi.  Then, complete a Gallery Walk and an assessment question.