Transformations
Transformations are the moves we make on shapes — and they are honestly one of the most enjoyable parts of the course. In this lesson Miss Jay Jay flips, turns, slides and resizes a triangle on the grid, one gentle step at a time. We reflect in the x-axis, the y-axis, the diagonals y = x and y = −x, and in vertical and horizontal lines, and learn to find a mirror line. We rotate through multiples of 90° about the origin and about other points, and find the centre and angle of a rotation. We translate with column vectors, and enlarge from a centre using whole-number and fractional scale factors, finding the scale factor and centre in reverse. Best of all, we master the skill the exam prizes most — describing any single transformation FULLY, with every detail its checklist demands.
By the end you should be able to (NSSCO Mathematics 9.2):
- Reflect a shape in the x-axis, the y-axis, the diagonals y = x and y = −x, and in lines of the form x = a and y = b
- Find the mirror line of a given reflection
- Rotate a shape about a given centre through multiples of 90°, stating the angle and direction
- Find the centre, angle and direction of a given rotation
- Translate a shape by a column vector, and find the vector connecting a shape to its image
- Enlarge a shape from a given centre using positive and fractional scale factors
- Find the scale factor and centre of a given enlargement
- Describe any single transformation fully, and identify invariant points