Under a *translation*, every point is moved by the *same amount* in the *same direction*. If each point moves distance *a* in the *x*-direction and distance *b* in the *y*-direction, we use the 'vector' notation to describe this translation.

For example, the translation described by the column vector is illustrated opposite; the translation moves the shape 6 units to the right and 2 units upwards.

Note that the actual shape *does not change its orientation*, only its position. It is *not reflected or rotated*.

What could each one of the following shapes be if it has 4 sides and:

(a)

Draw the square with corners at the points with coordinates (4, 0), (1, 3), (4, 6) and (7, 3).

(b)

The square is translated along the vector 52 . Draw the new square obtained by the translation.

For this translation each point should be moved 5 units to the right and 2 units up.

This diagram shows both squares and the vector that has been used to translate each corner.

The diagram below shows the shapes A, B, C and D. Along what vector would you translate:

(a) D to A, | (b) C to D, |

(c) A to B, | (d) A to C ? |

(a) | D to A | , | 10 to the right and 3 up. |

(b) | C to D | , | 1 to the right and 8 up. |

(c) | A to B | , | 5 to the right and 10 down. |

(d) | A to C | , | 11 to the left and 11 down. |