GCSE AQA Higher Further Maths · Topic 3 of 6
Choose a subtopic. Coordinate Geometry (2 dimensions only) covers Know and use the definition of a gradient, Know the relationship between the gradients of parallel and perpendicular lines, Use Pythagoras' theorem to calculate the distance between two points, and Use ratio to find the coordinates of a point on a line in GCSE AQA Higher Further Maths. 11 lessons in 9 subtopics.
Revise Coordinate Geometry (2 dimensions only) for GCSE AQA Higher Further Maths, including Know and use the definition of a gradient.
11
Lessons
9
Subtopics
Coordinate Geometry (2 dimensions only) has 9 subtopics, including:
11 lessons, grouped by subtopic.
Go back to the full GCSE AQA Higher Further Maths topic list, or practise this topic with past-paper questions.
Coordinate Geometry (2 dimensions only) covers Know and use the definition of a gradient, Know the relationship between the gradients of parallel and perpendicular lines, Use Pythagoras' theorem to calculate the distance between two points, and Use ratio to find the coordinates of a point on a line in GCSE AQA Higher Further Maths. 11 lessons in 9 subtopics.
Use Pythagoras' theorem: d = √((x₂ − x₁)² + (y₂ − y₁)²). The Distance Between Two Points Using Pythagoras notes cover this in full.
The distance between A(x₁, y₁) and B(x₂, y₂) is AB = √((x₂ − x₁)² + (y₂ − y₁)²). The Distance Between Two Points Using Pythagoras notes cover this in full.
Average the x-coordinates and average the y-coordinates: M = ((x₁ + x₂)/2, (y₁ + y₂)/2). The Dividing Lines in a Ratio notes cover this in full.
The gradient of a straight line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line, written m = rise ÷ run. The Understanding the Definition of a Gradient notes cover this in full.
Find the gradient of the radius to the point of contact, take its negative reciprocal for the tangent gradient, substitute into y − y₁ = m(x − x₁), then simplify. The Finding the Equation of a Tangent to a Circle notes cover this in full.
Two lines are perpendicular if the product of their gradients is −1: m₁ × m₂ = −1. The Parallel and Perpendicular Lines notes cover this in full.
Rise over run is the definition of gradient: the vertical change (rise) divided by the horizontal change (run) between any two points on a line, m = rise/run. The Understanding the Definition of a Gradient notes cover this in full.
A negative reciprocal is found by flipping a fraction and changing its sign. The Parallel and Perpendicular Lines notes cover this in full.