Translate a Shape
(KS3, Year 7)
The LessonA translation moves a shape. Every point of the shape is moved in the same direction by the same distance. To translate a shape, we need to move each point in the shape in a certain direction by a certain distance. To simplify translating a shape, we break the translation down into:
- How far we move the shape in a horizontal direction (left or right).
- How far we move the shape in a vertical direction (up or down).
Using a Column Vector to Translate a ShapeA column vector tells us how to translate a shape. A column vector shows two numbers, one above the other. An example of a column vector is shown below:
- The top number (4) tells us how much to move the shape in the horizontal direction (right if the number is positive, left if it is negative).
- The bottom number (2) tells us how much to move the shape in the vertical direction (up if the number is positive, down if it is negative).
How to Translate a ShapeTranslating a shape is easy.
QuestionTranslate the shape below using the column vector.
Step-by-Step:Let us start by choosing a point on the shape and translating it. We will translate point A.
Find the top number in the column vector. In our example, the top number is 4.
The number found in Step 1 (4) will tell us how to move point A in the horizontal direction. If the number is positive, the point is moved right. If the number is negative, the point is moved left. In our example, 4 is positive. Move point A 4 units to the right.
Find the bottom number in the column vector. In our example, the bottom number is 2.
The number found in Step 3 (2) will tell us how to move the point in Step 2 in the vertical direction. If the number is positive, the point is moved up. If the number is negative, the point is moved down. In our example, 2 is positive. Move the point 2 units up.
Lesson SlidesThe slider below shows another real example of how to translate a shape. Open the slider in a new tab
What Is a Translation?A translation is a slide of a shape: without rotating, reflecting or resizing it. A translation is a type of transformation.
Stick to the Point!When a shape is translated, each point in the shape moves the same direction and distance. When describing a translation, see how a single point has been moved. Choose a point on the shape, and see how it has moved after it has been translated.
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