Sliding a shape by a column vector, flipping it in a mirror line, and describing either one fully.
What you will learn
- Translate a point or shape by a column vector
- Reflect in x = a, y = b, y = x and y = −x
- Describe a translation or a reflection fully
A translation is a slide
A transformation moves a shape; the shape after the move is called the image (a point P moves to P′, read "P dash").
A translation moves every point the same distance in the same direction. The shape does not turn or flip, so the image is congruent to the original and the same way up. The movement is given as a column vector: the top number is the movement across (right is positive), the bottom number is the movement up (up is positive).
The vector 4−2 means 4 right and 2 down.
- P is (−1, 3); translate it by 4 across and −2 up
- x: −1 + 4 = 3
- y: 3 + (−2) = 1
- P′ is (3, 1)
To find the vector of a translation, pick one vertex and its image and count from the original to the image. Counting from the image back gives the vector with both signs wrong.
Two translations one after another add: 3 right and 1 up, then 2 left and 4 up, is 1 right and 5 up altogether. To go straight back to the start, change both signs of the total. To find the point before a translation, subtract the vector from the image: if Q′ is (1, 4) after a translation of 3 right and 2 down, then Q is (1 − 3, 4 − (−2)) = (−2, 6).
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- A translation is a slide
- A reflection is a flip
- The line people mix up
- Try it: Watch a point move
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Transformation, Image, Before, Vertical, Horizontal
In this unit: Transformations, congruence and similarity
Translations, reflections, rotations and enlargements on a grid and how to describe them fully, combined transformations and invariant points, the congruence conditions, and similar shapes with their length, area and volume scale factors.