Translations Wjec-Eduqas Foundation

Translations

What are transformations in maths?

• There are four transformations to learn

  • translations, rotations, reflections and enlargements

• A transformation can change the position, orientation and/or size of a shape

  • The original shape is called the object

  • The transformed shape is called the image

• Vertices are labelled to show corresponding points

  • Vertices on the object are labelled A, B, C, etc.

  • Vertices on the image are labelled A’, B’, C’ etc.

What is a translation?

• A translation moves a shape

• The size and orientation (which way up it is) of the shape stays the same

  • The object and image are congruent

What is a translation vector?

• The movement of a translation is described by a vector

• You need to know how to write a translation using a vector (rather than words)

• Vectors are written as column vectors in the form where:

  •  is the distance moved horizontally

    • Negative means move to the left

    • Positive means move to the right

  •  is the distance moved vertically

    • Negative means move down

    • Positive means move up

How do I translate a shape?

• STEP 1

  Interpret the translation vector

  • means 3 to the right and 1 down

• STEP 2
  Move each vertex on the original object according to the vector

• STEP 3
  Connect the new vertices and label the translated image

  • It should look identical to the original object just in a different position

• In some cases the image can overlap the object

How do I describe a translation?

• To describe a translation, you must:

  • State that the transformation is a translation

  • Give the column vector that describes the movement

• To find the vector:

  • Pick a point on the original shape

  • Identify the corresponding point on the image

  • Count how far left or right (<img alt=”x” data-mathml='<math ><semantics><mi>x</mi><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%2211%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3Etext%7Bfill%3A%23000000%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Time