Transformations and Vectors

You will be able to

• Draw the image of a shape after a reflection in a line such as x = k, y = k, y = x or y = −x, a rotation of 90° or 180° about a centre, or a translation by a column vector.
• Identify the invariant points of a transformation and state whether it keeps or reverses the orientation of a shape.
• Describe fully a single transformation that maps an object onto its image, giving every parameter.

You will be able to

• Enlarge a shape by a positive, fractional or negative scale factor about a given centre, using CP′ = k × CP.
• Find the centre and scale factor of an enlargement by joining corresponding points of the object and image.
• State that an enlargement multiplies lengths by |k| and areas by k², leaving angles unchanged so the image is similar to the object.

You will be able to

• Draw the image of a shape after two successive transformations, applying the first one first.
• Describe fully the single transformation equivalent to a combination of two transformations, or recognise when there is none.
• Explain, with an example, why the order in which two transformations are applied can change the result.

You will be able to

• Add and subtract column vectors, and multiply a column vector by a scalar, including a negative scalar.
• Represent a + b, a − b and ka on a grid using the triangle rule and the parallelogram rule.
• Calculate the magnitude of a column vector as √(x² + y²), giving the answer exactly as a surd or to 3 significant figures.

You will be able to

• Express a vector in terms of a and b by following a route of known vectors, reversing the sign when a vector is travelled backwards.
• Find the position vector of a point dividing AB in the ratio m : n, and of the midpoint of AB.
• Use scalar multiples and a common point to prove that three points are collinear.