Transformations & Vectors

Prerequisite Knowledge

• use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries;
• identify an order of rotational and reflective symmetry for two-dimensional shapes
• use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from the written description
• Recognise linear functions in the form y = ± a and x = ± a

Success Criteria

• identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional scale factors)
• apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors

Key Concepts

• An object is transformed to create an image.
• Rotation, Translation and Reflections involve congruent objects and images whereas enlargement leads to the object is similar to the image.
• Translation vectors are used to describe movements along Cartesian axes.
• When reflecting objects the image is always the same distance from the line of reflection as the object.
• Rotations and enlargements are constructed from a centre.
• A scalar has direction only whereas a vector has direction and magnitude.
• A vector has a magnitude and direction but its starting point is variable.
• Parallel lines have vectors that are multiples of each other.
• To add and subtract vectors is similar to collecting like terms.

Common Misconceptions

• Translation vectors can incorrectly be written using the name notation as coordinate pairs.
• Translations, Rotations, Enlargement and Reflections all come under the umbrella term of transformation. Students often confuse the term translation for transformation.
• Students often have more difficulty describing single transformations rather than performing them.
• Writing vectors in their simplest form by collecting like terms is often a problem in examinations.