Coordinate geometry

Learning objectives

Calculate the gradient, length and midpoint of a line segment, and use m₁ = m₂ for parallel lines and m₁m₂ = −1 for perpendicular lines

Find the equation of a straight line from two points or from a point and a gradient, in the form y = mx + c, y − y₁ = m(x − x₁) or ax + by + c = 0, including a perpendicular bisector

Find the centre and radius of a circle from (x − a)² + (y − b)² = r², or by completing the square on x² + y² + 2gx + 2fy + c = 0, and form the equation of a circle from given conditions

Use circle geometry — a tangent is perpendicular to the radius, the angle in a semicircle is a right angle and the perpendicular from the centre bisects a chord — to find tangents and unknown points

Find the points where lines, curves and circles intersect by solving simultaneously, and use the discriminant to decide whether a line meets, touches or misses a curve or circle