Coordinate geometry and plane vectors topic check · G3 Mathematics

Practise

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Coordinates and vectors

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Coordinates and vectors

Check your progress

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Coordinates and vectors

Find a finite line gradient from two given coordinate pairs · Check your progress

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Coordinates and vectors

Produce a line equation and its gradient/intercept from two given points · Check your progress

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Coordinates and vectors

Calculate the distance between two points · Check your progress

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Coordinates and vectors

Add vectors by ordered components · Check your progress

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Coordinates and vectors

Subtract vectors by ordered components · Check your progress

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Coordinates and vectors

Multiply a vector by a scalar · Check your progress

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Coordinates and vectors

Calculate the magnitude of a vector · Check your progress

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Coordinates and vectors

Find the directed displacement between two points · Check your progress

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Coordinates and vectors

Translate a coordinate point by a directed vector · Check your progress

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Coordinates and vectors

Express a directed displacement in two nonparallel named vectors · Check your progress

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Coordinates and vectors

Check again

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Coordinates and vectors

Find a finite line gradient from two given coordinate pairs · Check again

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Coordinates and vectors

Produce a line equation and its gradient/intercept from two given points · Check again

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Coordinates and vectors

Calculate the distance between two points · Check again

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Coordinates and vectors

Add vectors by ordered components · Check again

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Coordinates and vectors

Subtract vectors by ordered components · Check again

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Coordinates and vectors

Multiply a vector by a scalar · Check again

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Coordinates and vectors

Calculate the magnitude of a vector · Check again

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Coordinates and vectors

Find the directed displacement between two points · Check again

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Coordinates and vectors

Translate a coordinate point by a directed vector · Check again

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Coordinates and vectors

Express a directed displacement in two nonparallel named vectors · Check again

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Coordinates and vectors

Retention check

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Coordinates and vectors

Find a finite line gradient from two given coordinate pairs · Retention check

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Coordinates and vectors

Produce a line equation and its gradient/intercept from two given points · Retention check

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Coordinates and vectors

Calculate the distance between two points · Retention check

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Coordinates and vectors

Add vectors by ordered components · Retention check

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Coordinates and vectors

Subtract vectors by ordered components · Retention check

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Coordinates and vectors

Multiply a vector by a scalar · Retention check

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Coordinates and vectors

Calculate the magnitude of a vector · Retention check

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Coordinates and vectors

Find the directed displacement between two points · Retention check

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Coordinates and vectors

Translate a coordinate point by a directed vector · Retention check

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Coordinates and vectors

Express a directed displacement in two nonparallel named vectors · Retention check

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Coordinates and vectors

Practise: Find a finite line gradient from two given coordinate pairs

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Coordinates and vectors

Practise: Produce a line equation and its gradient/intercept from two given points

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Coordinates and vectors

Practise: Calculate the distance between two points

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Coordinates and vectors

Practise: Add vectors by ordered components

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Coordinates and vectors

Practise: Subtract vectors by ordered components

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Coordinates and vectors

Practise: Multiply a vector by a scalar

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Coordinates and vectors

Practise: Calculate the magnitude of a vector

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Coordinates and vectors

Practise: Find the directed displacement between two points

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Coordinates and vectors

Practise: Translate a coordinate point by a directed vector

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Coordinates and vectors

Practise: Express a directed displacement in two nonparallel named vectors

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Coordinates and vectors

Revision notes

Revise coordinates and vectors

Connect straight-line equations with coordinate geometry, then use plane vectors and scalar multiples to justify geometric relationships.

Key ideas

Straight lines and coordinate lengths
Connect line equations, gradients and distance with coordinate differences.
Plane vectors and geometric arguments
Use displacement, position and scalar multiples consistently to justify geometric relationships.

What the syllabus asks

From the G3 Mathematics 2027 syllabus

Show all 12 syllabus statements

Finding the gradient of a straight line given the coordinates of two points on it
Finding the length of a line segment given the coordinates of its end points
Interpreting and finding the equation of a straight line graph in the form y = mx + c
Geometric problems involving the use of coordinates
Use of column-vector notation (x, y), vectors AB and a, and magnitudes |AB| and |a|
Vector as a directed line segment
Translation by a vector
Position vectors
Magnitude √(x² + y²)
Sum and difference of vectors to express given vectors in terms of two coplanar vectors
Scalar multiplication
Geometric problems using vectors

Check what you know

Your question

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Starting check complete

Next steps

Where marks were lost

Your answers

Revise coordinates and vectors

Key ideas

What the syllabus asks