About this topic
Before you begin
Connect straight-line equations with coordinate geometry, then use plane vectors and scalar multiples to justify geometric relationships.
Learning goals
- Find a finite line gradient from two given coordinate pairs
- Produce a line equation and its gradient/intercept from two given points
- Calculate the distance between two points
- Reason and calculate using coordinate geometry
- Add vectors by ordered components
- Subtract vectors by ordered components
- Multiply a vector by a scalar
- Calculate the magnitude of a vector
- Find the directed displacement between two points
- Translate a coordinate point by a directed vector
- Express a directed displacement in two nonparallel named vectors
- Represent and calculate with plane vectors
Syllabus statements covered
- 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
- 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 notations: column vector (x, y), vector AB, vector a, magnitude |AB| and |a|
- Representing a vector as a directed line segment
- Translation by a vector
- Position vectors
- Magnitude of a column vector (x, y) as √(x² + y²)
- Use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors
- Multiplication of a vector by a scalar
- Geometric problems involving the use of vectors
Choose a lesson
Work through them in order.