Comparing and applying transformations

General Information
"Compare and apply single and multiple transformations." Is a bullet point under Geometry and Measurement of Level 6 Mathematics and Statistics. Being what creates similar and congruent triangles, this, although rarely assessed on its own, is a very important thing to know.

What you need to know
There are four main types of transformations: Rotation, Reflection, Translation and Enlargement. Rotation, reflection and translation result in a shape of the same size as the origional, while enlargement creates a shape of a different size.

Rotation of a shape is done around a center of rotation, usually plotted on a graph. The distance between any of the shape's points and the center point stays the same after a rotation, but all the points move in a curve of a certain angle around the center point. The point (5,0) rotated 90.around the origin will end up at (0,5).

Reflection of a shape occurs around a line of reflection. The distance between each point and the line of reflection also stays the same before and after reflection, but all the points are moved to the other side of the line. The point (3,1) mirrored around the line x=0 would end up at (-3,1).

Translation of a shape occurs for a certain distance, in a certain direction. Each point of a shape is moved in that direction, for that distance. This results in a shape with the same shape, size and rotation, but in a different position. The point (0,0) translated 3 points to the right and 4 points up would end up at (3,4).

Enlargement, also called a variety of other names, is the enlargement of a shape (duh) with a center of enlargement. Enlargements have a scale factor, determining how the shape is changed. The distance betewen each point of the origional shape and the center of enlargement is multiplied by the scale factor to fin the distance between the points of the new shape and the center of enlargement, and thus the position of the new shape.

Practice Questions

 * 1) Translate the point (2018,2957) 2 point up and 4 point to the right.
 * 2) Rotate the point (1,2) 270.around the origin.
 * 3) Reflect the point (3,4) around the line y=2

Answers

 * 1) (2022,2959)
 * 2) (-2,1)
 * (3,0)

Helpful Links
https://revisionmaths.com/gcse-maths-revision/shape-and-space/transformations (tutorial on transformations)

https://www.mathsisfun.com/geometry/transformations.html (Random interactive stuff)

https://www.khanacademy.org/math/geometry/hs-geo-transformations (lessons, videos and practice all in one!)