How to Translate a Shape

Translating a Shape

A 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 Shape

A 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 Shape

Translating a shape is easy.

Question

Translate 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.

1

Find the top number in the column vector. In our example, the top number is 4.

2

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.

3

Find the bottom number in the column vector. In our example, the bottom number is 2.

4

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.

Point A has been translated to to find A', the corresponding point on the translated shape.

Repeat the Steps for Points B and C.

Answer:

Slider

The slider below shows another real example of how to translate a shape.

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See Also

What is geometry? What are transformations? Translating a shape using Cartesian coordinates What is a positive number? What is a negative number?