Translating Shapes
Translating a shape slides it across a grid, keeping its size and orientation the same. All vertices move the same way. A column vector like (3, 2) describes the translation: 3 right, then 2 up.
Video Lesson
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Translation: Sliding a Shape
- A translation moves a shape without changing its size or orientation.
- Every point shifts the same distance in the same direction.
Column Vectors
- The top number shows the horizontal movement, where positive is right and negative is left.
- The bottom number shows the vertical movement, where positive is up and negative is down.
Translating 2D Shapes
- You move all vertices using the same column vector, then connect them.
- The shape stays identical, just in a new position.
Finding the Column Vector
- Count how far a point moves left or right first.
- Then count how far it moves up or down.
Practice Questions
Test your understanding
What does column vector mean?
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The negative value (−4) tells us to move 4 units left, and the positive value (2) tells us to move 2 units up.
What does column vector mean?
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The negative value (−3) tells us to move 3 units left, and the negative value (−6) tells us to move 6 units down.
Shape A is translated to Shape B by moving 7 units to the right and 3 units down. What is the column vector for this translation?
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The positive 7 on the top means moving 7 units to the right, and the −3 at the bottom means moving 3 units down.
Write down the column vector shown in the diagram.
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To read a column vector from a diagram, start at the beginning of the arrow. First count the horizontal movement. It is 5 units to the left, so the top number is -5. Then count the vertical movement. It is 2 units down, so the bottom number is -2. That gives the vector .
A point starts at (2, 5) and is translated using the column vector . What are the new coordinates of the point?
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To find the new coordinates, subtract 3 from the x-coordinate: and subtract 4 from the y-coordinate: , which gives (−1, 1).
Shape M is translated to Shape N as shown in the diagram. Find the column vector for this translation.
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To find the column vector, count the horizontal movement (5 units left) and the vertical movement (3 units up). This gives the vector .
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Interactive Activity
Translate shapes with column vectors on a grid
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Students Also Ask
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No. A translation only slides the shape to a new position on the grid. Its size, shape, and orientation stay exactly the same. Every point moves the same distance in the same direction, so the shape looks identical, just in a different place.
A translation vector is a column vector that describes a translation. The top number tells you how far to move the shape horizontally. The bottom number tells you how far to move it vertically. Together they give a precise instruction for the slide.
The top number, labelled a, tells you how many units to move horizontally, either left or right. The bottom number, labelled b, tells you how many units to move vertically, either up or down. Together they give a precise instruction for shifting a shape across the grid.
In the top number, a positive value means move right and a negative value means move left. In the bottom number, a positive value means move up and a negative value means move down. The signs set the direction of each movement.
Shift every corner of the shape by the amounts in the column vector. Move each corner horizontally by the top number, then vertically by the bottom number. Mark the new corner positions, then connect them in the same order to draw the translated shape.