Geometry and measures - Vectors: describe translations as 2D vectors

The idea

A translation slides every point of a shape the same distance in the same direction, so the image is congruent to the object and keeps the same way up. You record the slide as a column vector: the top number is the movement right, negative for left, and the bottom number is the movement up, negative for down. To translate a shape, move each vertex by that vector and join the images. To describe a translation you are shown, pick one vertex and the matching vertex on the image, then count across first and up second. If a corner at the point with coordinates one and four maps to the corner at six and two, the movement is five right and two down, so the top number is five and the bottom number is negative two.

What earns the marks

• The word translation when the question asks you to describe the transformation, and a further mark for the column vector that goes with it.
• A column vector with the horizontal component on top and the vertical component below.
• A column vector carrying the correct signs, negative for a movement to the left and negative for a movement down.
• An image drawn the same size and the same way up as the object, in the right position on the grid.

Common mistakes and how to put them right

• Writing the vertical movement on top and the horizontal movement below, which sends the image somewhere else entirely.

• Giving a positive bottom number for a downward movement, or a positive top number for a movement to the left.

• Calling the transformation a move, a shift or a slide rather than naming it a translation, which loses the naming mark.

• Counting between a vertex of the object and the wrong vertex of the image, so the vector is right in shape but wrong in size.

Exam tips

• Mark one vertex on the object and the matching vertex on the image, then count across and only then count up. That is the order the column vector is written in.
• Check your image by translating a second vertex the same way. If the two do not agree you have miscounted before you have drawn anything wrong.
• When asked for a single transformation, specify one transformation completely; a sequence of transformations does not answer that instruction.