Concepts Of Coordinate Geometry

 

Coordinate geometry gives us a way to describe exact position on a plane surface, is by using two numbers.

Definition: A system of geometry where the position of points on the plane is described using an ordered pair of numbers.

Co-ordinates

Look at the grid shown above. The columns of the grid are lettered A, B, C D, E, F. The rows are numbered from 1 to 6 from the top. We can see that the X is in box D3; that is, column D, and row 3.

D and 3 are called the coordinates of the box. It has two parts: the row and the column. There are many boxes in each row and many boxes in each column. But by having both we can find one single box, where the row and column intersect.

The Coordinate Plane

In coordinate geometry, points are placed on the "coordinate plane" as shown below. It has two scales - one running across the plane called the "x axis" and another a right angles to it called the y axis. The point where the axes cross is called the origin and is where both x and y are zero.

On the x-axis, values to the right are positive and those to the left are negative.

On the y-axis, values above the origin are positive and those below are negative.

A point's location on the plane is given by two numbers,the first tells where it is on the x-axis and the second which tells where it is on the y-axis. Together, they define a single, unique position on the plane. As per the the diagram above, the point A has an x value of 20 and a y value of 15. These are the coordinates of the point A, sometimes referred to as its "rectangular coordinates". The x coordinate is always the first one of the pair.

When you know the coordinates of a group of points you can:

  • Determine the distance between them.
  • Find the midpoint, slope and equation of a line segment.
  • Determine if lines are parallel or perpendicular.
  • Find the area and perimeter of a polygon defined by the points.
  • Transform a shape by moving, rotating and reflecting it.
  • Define the equations of curves, circles and ellipses.