Vectors: describe translations as 2D vectors

The idea

A translation moves every point of a shape by the same distance and direction, described using a 2D column vector. The vector is written as a column with horizontal movement on top and vertical below. For example, a vector with 3 on top and -2 below means move 3 units right and 2 units down. The top number is positive for right, negative for left; the bottom is positive for up, negative for down. To describe a translation from a diagram, compare a vertex on the object with its corresponding image vertex. Subtract the object coordinates from the image coordinates to find the vector. The shape does not rotate or reflect, so the image is congruent. This vector applies equally to all points on the shape.

What earns the marks

• Writes a translation as a 2D column vector with the horizontal component on top and the vertical component below.
• Interprets the signs correctly: positive top means right, negative top means left, positive bottom means up, negative bottom means down.
• Describes a translation from a diagram by comparing a vertex on the object with its image and subtracting coordinates.
• Recognises that a translation produces a congruent image with the same orientation, not a rotation or reflection.

Common mistakes and how to put them right

• Swapping the components: the top number is always the horizontal movement and the bottom number is always the vertical movement, so a vector with 3 on top and -2 below is not the same as -2 on top and 3 below.

• Reversing the signs: moving left or down needs a negative component, so a translation 3 left and 2 up has -3 on top and 2 below, not 3 and 2.

• Describing a translation as a rotation or reflection.

  Put it right: A translation only slides the shape, so the image is congruent and has the same orientation.

• Subtracting coordinates in the wrong order when finding the vector.

  Put it right: Use image coordinates minus object coordinates, not the other way round.

Exam tips

• Label the object and image vertices (for example A and A') so you can compare matching points accurately.
• Check the direction of each component against the grid: right and up are positive, left and down are negative.
• Write the vector as a column, not a row, and keep the horizontal component on top.