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:
How to Translate a Shape
Translating a shape is easy.
Question
Translate the shape below using the column vector.
StepbyStep:
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.