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Mathematics · Year 10 · Path · MA5-LIN-P-01

Linear Relationships C

Fifteen lessons that turn the coordinate plane into a place where geometry can be argued rather than only drawn. The Core work found midpoints, gradients and distances by counting squares; this area turns each of those processes into a formula, then spends the rest of its time on what formulas make possible: equations of lines, proofs about figures, symmetry, and the four transformations.

15lessons
25syllabus points
10-11hstudy
Start Lesson 1 →
1
The Midpoint Formula
An average taken twice, and the parallelogram test it makes possible
2
The Gradient Formula
Rise over run written as a subtraction, plus the zero and undefined cases
3
The Distance Formula
Pythagoras theorem on a triangle you draw yourself under the interval
4
Forms of the Equation of a Line
Gradient-intercept and general form, and the letter that means two things
5
Intercepts and Sketching
Substitute the variable you are not looking for, and the three cases that resist
6
Point-Gradient Form
The gradient formula with the fraction cleared, and one point to fix position
7
The Line Through Two Points
Two formulas in sequence, and the unused point as a free check
8
Parallel and Perpendicular Lines
Equal gradients, or a product of minus one, and the pair the rule cannot reach
9
Coordinate Geometry Problems
The word in the question names the formula; classification, perimeter and area
10
Proving Facts About Figures
Sufficient tests rather than consistent ones, and medians against altitudes
11
Line and Rotational Symmetry
Folds and turns counted separately, because neither implies the other
12
Symmetry in Graphs
Substitute the image of a point and see whether the equation survives
13
Translations and Image Notation
One arrow applied to every point, and what the dash in P dash means
14
Reflections in the Axes
The mirror names the coordinate that survives, and orientation reverses
15
Rotations About the Origin
Swap the coordinates and fix one sign; rebuild each rule from two points

Focus Area Snapshot

15lessons
25syllabus points
45worked examples
120questions

Where this leads

This is a Path focus area, sitting outside the Core and preparing you for Mathematics Advanced in Year 11. Almost none of it is ever retired. The three formulas and the equation forms are used in every senior coordinate geometry question, and the habit built here, of naming the property that justifies a conclusion rather than only computing, is what senior proof questions are marked on.

Start Lesson 1 →