Coordinate Geometry in the (x, y) Plane

Basic Concepts and Formulas

Gain a deep understanding of the Cartesian coordinate system in a 2D space, which includes the x-axis, y-axis, origin and the four quadrants.
Learn how to plot points in the x, y plane and determine their coordinates.
Understand the concept of distance between two points using the distance formula.
Get familiar with the midpoint formula which is used to find the coordinates of the point that is exactly halfway between two given points.

The Equation of a Line

Learn how to derive the equation of a line given two points, the slope and a point, or the y-intercept and the slope.
Develop proficiency in using different forms of a linear equation: slope-intercept form, point-slope form, and standard form.
Understand the concept of parallel and perpendicular lines and their slopes. Parallel lines have the same slope, whereas slopes of perpendicular lines are negative reciprocals of each other.
Be able to rewrite linear equations in different forms, and transition between forms as needed.

Circles

Understand the standard form of the equation of a circle, which is (x-h)² + (y-k)² = r², where (h,k) are the coordinates of the centre and r is the radius of the circle.
Be able to find the centre and radius of a circle given its equation.
Learn how to derive the equation of a circle given the centre and a point on the circle, or given the diameter’s endpoints.

Analytical Geometry

Use algebraic methods to solve geometrical problems, such as finding the intersection points of lines and circles, or determining whether a point lies on a line or inside, outside or on a circle.
Familiarise yourself with the concept of locus and use it to solve complex problems in Coordinate Geometry.

Remember, these bullet points are provided to aid your revision and should be supplemented with class materials, textbooks, and other resources for a thorough understanding of the topic. Ensure to practise a lot of problems to better grasp the concepts.