Geometry

Properties of straight line segments

Properties of straight line segments. In this unit a system of co-ordinates is described, and is used to find various properties of the straight line between two points. The distance between the two points and the mid-point of the line joining the two points are calculated.

The gradient of a straight line segment

The gradient of a straight line segment. In this unit the gradient of a straight line segment is found, and the relationships between the gradients of parallel lines and perpendicular lines are explained.

Equations of straight lines

Equations of straight lines. In this unit the equation of a straight line is established using either information about its gradient together with the co-ordinates of a point on the line, or alternatively the co-ordinates of two different points on the line. The different ways of expressing the final equation are explored.

The Geometry of a Circle

The geometry of a circle. In this unit the equation of a circle is found from the co-ordinates of its centre and its radius. There are two different forms of the equation. The unit also covers some examples involving tangents to circles.

Conic Sections

Conic sections. Conic sections are the curves obtained when a cone is cut by a plane. The equation of one of these curves, the parabola, is found by using an alternative description in terms of points whose distances from a fixed point and a fixed line are equal.

Polar Co-ordinates

Polar co-ordinates . The (x, y) co-ordinates of a point in the plane are called its Cartesian co-ordinates. But there is another way to specify the position of a point, and that is to use polar co-ordinates. Conversion from Cartesian co-ordinates to polar co-ordinates, and back again, is explained.