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