MathematicsExam code: 0580

Transformations

Vectors and Transformations

PractiseFlashcards

Doing and describing one

  • A translation slides the shape without turning or resizing it, so the orientation is unchanged
  • The movement is given as a column vector, with the top number the horizontal move and the bottom number the vertical one
  • Positive top means right and negative means left; positive bottom means up and negative means down
  • Move every vertex by the same vector, then join them up
Shape P translated to its image P prime, with a red stepped path drawn from one vertex of P to the matching vertex of P prime, counting the horizontal steps first and then the vertical ones
Source: Translations by Save My Exams
  • To describe one, say translation and give the vector
  • Mark schemes also accept the movement in words, such as "2 right, 7 down"
Shape A translated to shape B, with a red stepped path drawn between one pair of matching vertices and annotated 2 right and 3 down, which is the column vector of the translation
Source: Translations by Save My Exams

Worked example

Translating by a column vector

Triangle A has vertices (5, 1), (9, 1) and (9, 3). Draw the image of A after a translation by the column vector with top number −4 and bottom number 5.

Solution:

  • The top number −4 means 4 squares to the left, and the bottom number 5 means 5 squares up
  • Move every vertex by the same amount: (5, 1) goes to (5 − 4, 1 + 5) = (1, 6)
  • In the same way, (9, 1) goes to (5, 6) and (9, 3) goes to (5, 8)
  • Join the three points with a ruler: the image has vertices (1, 6), (5, 6) and (5, 8)
  • Check: the image is the same size, shape and way round as A, and its base from (1, 6) to (5, 6) is horizontal and 4 long, like A's base from (5, 1) to (9, 1)
Triangle A with vertices (5, 1), (9, 1) and (9, 3) and its image A′ with vertices (1, 6), (5, 6) and (5, 8), with arrows from (5, 1) going 4 squares left and then 5 squares up to (1, 6)

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