Coordinate Geometry

Success Criteria

At the end of this chapter, students are able to:

  1. Calculate the angle of inclination for a line with a given gradient (and vice-versa).

  2. Apply the relationship of gradients of parallel lines.

  3. Apply the relationship of gradients of perpendicular lines.

  4. Find the midpoint of 2 given points.

  5. Find the area of a polygon using the shoelace method given the coordinates of the vertices.

  6. Prove that a triangle is a right-triangle (AO3).

  7. Find the centre and radius of a circle given the equation of a circle (and vice-versa).

  8. Find the equation of a circle after simple transformations.

  9. Find the equation of the tangent to a circle at a point.

  10. Find the equation of a circle given 3 points on the circumference.

  11. Determine and justify if a point lies inside or outside a circle (AO3).

Recap

From the Elementary Mathematics Chapter on Coordinate Geometry, you should already be able to:

  1. Find the length of a line segment.

  2. Find the gradient of a straight line.

  3. Find the equation of a straight line.