Sectieoverzicht

  • Coordinate Geometry (also called analytical geometry) is the study of geometric objects and shapes (points, lines, quadrilaterals, etc.) on the Cartesian (coordinate) plane. 

    The Cartesian plane is a two-dimensional surface defined by two perpendicular number lines, which we call axes. The horizontal axis (running from left to right) is the x-axis and the vertical axis (running from top to bottom) is the y-axis. Each axis extends forever in both directions this is why we draw them with arrows on the ends.

    We call the point where the axes meet the origin.

    The Cartesian plane


    We can describe the position of any point on the Cartesian plane with an ordered pair. The first number is the x-coordinate (how far left or right of the origin the point is) and the second number is the y-coordinate (how far up or down from the origin the point is).

    The Cartesian plane has four quadrants as shown in the diagram.

    In the diagram we can see the point P with coordinates (-1; -2) is plotted in the third quadrant. The point P is 1 unit to the left from the origin and 2 units down from the origin.

    Try the next activity to test your knowledge on plotting points by dragging the coordinates to the letters on the Cartesian plane. 


    • Leerlingen moeten
      Als voltooid aanduiden

      Exercise: Plot points from a table

      1. Plot the coordinate pairs shown in the table. 

      Table with x and y coordinates

      2. Join the dots. What do you notice?

      3. Find an equation that relates \(x\) to \(y\).

      Solution

      2. If we join the dots we see that the points all lie on the same straight line as shown in the diagram.

      Plotted points on a straight line

      3. The equation that relates \(x\) to \(y\) is \(y=x+1\).