Lesson: Challenging Problem Solving - 35

Advanced Geometry: Coordinate Geometry

But coordinate geometry doesn't have to be difficult; not all coordinate geometry questions require algebra. In fact, many are quite similar to regular geometry questions, and your knowledge of triangles, rectangles and circles will help you through many of these problems.

A few key facts will provide you with the background you need to manage coordinate geometry. Let's review these key facts briefly, and then move on to an example:

• Coordinate geometry is based on a coordinate plane of 4 quadrants formed by 2 axes, an x-axis and a y-axis.
• Points may be plotted on each of the quadrants. Each point is represented by the coordinate pair (x, y).
• To find the distance between any two points that do not share a coordinate, form a right triangle and use the Pythagorean theorem.
• The degree of the rise or fall of a line on the coordinate plane is the slope.
  The slope of a line is the ratio where (x₁, y₁) and x₂, y₂ are points on the line. This ratio holds for all points on the line.

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