Select a course.
arrow_back
Foundation plus - Transformations
infoWhy this? We are teaching this unit so that pupils can perform and describe transformations and vectors on coordinate grids, enabling them to represent and manipulate shapes precisely and understand how geometric objects change and what stays the same
scheduleWhy now? We are teaching it now in Year 10 so that pupils can use transformation and vector skills to deepen their current work in geometry and algebra, particularly when reasoning about symmetry, similarity and movement in more complex diagrams
neurologyYou need to know
- A rotation moves every point of an object around a fixed point (the centre of rotation) by a given angle and direction (clockwise or anticlockwise).
- A reflection creates a mirror image of an object in a given line (mirror line), which can be horizontal, vertical, or diagonal (e.g., (y = x), (y = -x), or (y = mx + c)).
- A translation moves every point of an object the same distance in the same direction, described by a translation vector
- An enlargement changes the size of an object by a scale factor, with respect to a centre of enlargement. The scale factor can be positive, negative, or fractional.
- The scale factor of enlargement is the ratio of the lengths of corresponding sides in the image and the object.
- A fractional scale factor produces an image smaller than the original object.
- A negative scale factor produces an image on the opposite side of the centre of enlargement.
- Multiple transformations can be performed in sequence, and the order of transformations affects the final result.
- Vectors represent movement or displacement and can be written in column form }).
- Vectors can be added or subtracted by combining their components, and multiplied by a scalar to change their magnitude.
- Some properties, such as shape and orientation, may change under transformations, while others, such as length and angle, may remain invariant.
- Invariance refers to properties that do not change under a transformation or combination of transformations.
rocket_launchYou must be able to
- Rotate an object about a fixed coordinate on a coordinate grid by a given angle and direction.
- Reflect an object in any horizontal or vertical line, or in the lines (y = x), (y = -x), or (y = mx + c) on a coordinate grid.
- Translate an object on a coordinate grid using a translation vector.
- Enlarge an object by a given scale factor using a given coordinate as the centre of enlargement.
- Identify the scale factor of enlargement when given an object and its enlargement.
- Describe fully a translation using a translation vector on a coordinate grid.
- Describe fully a rotation, including the centre, angle, and direction, on a coordinate grid.
- Describe fully a reflection, including the equation of the mirror line, on a coordinate grid.
- Describe fully an enlargement, including the centre and scale factor, on a coordinate grid.
- Interpret and use fractional scale factors for enlargements.
- Interpret and use negative scale factors for enlargements.
- Perform multiple transformations on an object, in the correct order.
- Add and subtract vectors and multiply vectors by a scalar using both diagrammatic and column representations.
- Describe the changes and invariance achieved by combinations of rotations, reflections, and translations.
Revision Quiz
trophy
Congratulations! You have completed the quiz.