Coordinate Geometry in the (x, y) Plane

Understanding Coordinates

Understand the two-dimensional coordinate system, which includes the x-axis (horizontal) and y-axis (vertical).
Interpret coordinates (x, y), where x represents how far along and y represents how far up or down the point is on the grid from the origin (0, 0).
Recall that coordinates in the four quadrants have different combinations of positive and negative values: top-right (positive, positive), top-left (negative, positive), bottom-left (negative, negative), and bottom-right (positive, negative).
Understand that the x-coordinate is also referred to as the abscissa and the y-coordinate as the ordinate.

Equation of a Line

Use the equation of a line in the form y = mx + c, where m is the gradient and c is the y-intercept.
Differentiate between horizontal and vertical lines; the former having the equation in the form y = c and the latter as x = c.
Know that two lines with equal gradients are parallel, and lines are perpendicular if the product of their gradients is -1.
Figure out the equation of a line given two points on the line.

Distance Between Two Points

Use the formula √[(x2 - x1)² + (y2 - y1)²] to calculate the distance between two points (x1, y1) and (x2, y2).

Mid-point of Two Points

Use the formula [(x1 + x2)/2, (y1 + y2)/2] to find the mid-point of a line segment defined by two points (x1, y1) and (x2, y2).

Circle Equation

Understand the standard form of the circle equation (x - a)² + (y - b)² = r², where (a, b) is the centre and r is the radius.
Plot a circle on the coordinate plane using its centre and radius.
Work out the equation of a circle given its centre and one point on the circumference.

Intersections

Solve the equations of a line and a curve to determine the intersection points.
Understand that a tangential line to a curve at a point is the straight line that “just touches” the curve at that point, meaning it intersects the curve at exactly one point.