Vectors and conics
Vectors and conics

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Vectors and conics

1 Coordinate geometry: points, planes and lines

1.1 Points, lines and distances in two-dimensional Euclidean space

In coordinate geometry we generally use rectangular (or Cartesian) coordinate axes, as illustrated below, to describe the Euclidean plane. We can represent any point in the plane uniquely by an ordered pair of coordinates (a, b); that is, any point in the plane has precisely one possible pair of coordinates with respect to the chosen axes.

This gives a one-one correspondence between the points of the plane and ordered pairs of real numbers. Often we do not bother to distinguish explicitly between the points and their representation as ordered pairs; we simply write (a, b) to denote the point A.

The plane together with an origin and a pair of x-, y-axes is often called two-dimensional Euclidean space, denoted by the symbol 2.


Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus