Coordinate Geometry

When you begin the study of Coordinate Geometry it is hard to not appreciate the great genius of Rene Descartes.  In math circles Descartes is known as the father of coordinate geometry (also known as analytic geometry).  Coordinate geometry merges concepts from algebra and geometry and has many applications. Today the ideas of coordinate geometry are widely used in physics and engineering.  An understanding of coordinate geometry is essential for success in the study of other fields of geometry, for example, algebraic, differential, discrete and computational geometry.

When I designed the iPad app, Coordinate Geometry, I wanted to create a highly interactive environment for learning the basic ideas.  Usually teachers begin with an explanation of the coordinate system.  In the design of the app I used a metaphor of a table top with a slightly transparent grid.  The center of the grid is the origin and ‘origin’ is one of the many vocabulary words that a teacher would want students to learn in reference to coordinate geometry. From the origin, the grid lines are typically numbered with positive integers to the right and up.  The grid lines to the left and also below the origin are labeled with negative integers. The horizontal line passing through the origin is the x-axis and the vertical line is the y-axis.  This divides the coordinate plane into four sections.  Conceptually the x and y axes are infinite. Traditionally the sections are labeled with Roman numerals.  Tapping the little dog-ear icon at the bottom right of the grid labels the sections according to the standard mathematical conventions. Points are referenced using a coordinate pair where the corresponding position on the x-axis is given first and then the y-axis with the two numbers separated by a comma and enclosed within parentheses. If the x and y coordinates are both positive the point lies in Quadrant I.  Likewise if x is negative, and y is positive, the point lies in Quadrant II.

At the bottom left of the screen are three tools, the line, the rectangle and the circle.  By selecting one of these tools, students can draw figures on the grid.  Because Coordinate Geometry is designed as an open-ended teaching resource, teachers can direct the students to complete various task just be given oral or written instructions.  For example:

1. Draw a line segment from (-6,-6) to (6,6).  Which special point does this line pass through?  (origin)
2. Draw a square on the grid.  List the coordinates of the vertices.
3. Draw a circle with the center at (3,3) and a radius of 4 units.

In addition to the many teacher-designed lessons that can be carried out using Coordinate Geometry, there are built-in lessons that can be accessed by tapping the lesson icon. I wanted to also include some self-checking challenges for students.  When the question icon is tapped, the app automatically displays a quiz question. The quiz questions are randomly generated so a unique set of questions is presented each time the quiz is accessed. The main topics that can be explored with the Coordinate Geometry app are:

• Coordinate Plane
• x and y axes
• Origin (0,0)
• Coordinate Pairs