Year 5 Maths: Translation Using a Co-ordinate Grid

Introduction to Translation

Understanding the Co-ordinate Grid

A co-ordinate grid looks like a big square made up of smaller squares. It has two lines called axes:

• The horizontal line (going left to right) is called the x-axis.
• The vertical line (going up and down) is called the y-axis.

Each point on the grid has a pair of numbers called coordinates. For example, if a point is at (3, 2), it means:

• Move 3 spaces to the right on the x-axis.
• Move 2 spaces up on the y-axis.

Here’s what it looks like:

     y     |   4 |      ● (3, 4)   3 |    2 |    ● (3, 2)   1 |    0 |_________________ x     0  1  2  3  4 

What is Translation?

Translation is moving a shape from one place to another on the grid. We can describe the move using vector notation. A vector tells us how far to move in the x direction and how far to move in the y direction.

For example, if we have a vector of (2, 1), this means:

• Move 2 spaces to the right (positive x direction).
• Move 1 space up (positive y direction).

Key Rules for Translation

1. Keep the shape the same: The sides and angles of the shape do not change.
2. Use a vector to describe the move: Write it like this: (x, y).
3. Add the vector to the original coordinates:
   • New x-coordinate = Original x-coordinate + x part of the vector
   • New y-coordinate = Original y-coordinate + y part of the vector

Example of Translation

Let’s take a triangle located at points A(1, 1), B(1, 4), and C(4, 1).

If we want to translate it using the vector (2, 3):

1. Move point A (1, 1):
   • New A = (1 + 2, 1 + 3) = (3, 4)
2. Move point B (1, 4):
   • New B = (1 + 2, 4 + 3) = (3, 7)
3. Move point C (4, 1):
   • New C = (4 + 2, 1 + 3) = (6, 4)

So the new triangle will be at A(3, 4), B(3, 7), and C(6, 4).

Tips and Tricks

• Always start by plotting your original shape.
• Write down the coordinates before and after translation.
• Use graph paper to help you keep your shapes neat and in line.

Practice Questions

Easy Level Questions

1. Translate the point (2, 3) by the vector (1, 1).
2. What are the new coordinates of (0, 0) after translating by (4, 2)?
3. Translate the point (5, 5) by (0, -3).
4. What is the new location of (3, 2) after a translation of (-1, 1)?
5. If you translate (2, 2) by (2, 0), what are the new coordinates?
6. Move the point (1, 1) by (3, 2). What do you get?
7. Translate (4, 4) by (0, 1). What are the new coordinates?
8. If (3, 3) is translated by (1, -1), where does it go?
9. What are the new coordinates of (0, 1) after moving it by (2, 2)?
10. Find the new position of (5, 0) after a translation of (-2, 3).

Medium Level Questions

11. Translate the point (2, 5) by the vector (3, -2). What are the new coordinates?
12. If point A is at (1, 2) and is translated by (2, 3), where does point A go?
13. What are the coordinates of point (3, 3) after a translation of (-1, 2)?
14. Translate the point (4, 0) using the vector (0, -4).
15. If (2, 4) is moved by (3, 3), what are the new coordinates?
16. Move the point (5, 5) by (-3, 1). What are the new coordinates?
17. Translate (1, 0) by (2, -2). Where does it end up?
18. If point B is at (6, 6) and is translated by (-2, 0), where does point B go?
19. What are the new coordinates after translating (0, 3) by (5, 2)?
20. Translate (3, 2) by (1, 1). What are the new coordinates?

Hard Level Questions

21. Translate the triangle with vertices A(1, 1), B(1, 3), C(4, 1) using the vector (2, 2). What are the new coordinates?
22. If point P is at (0, 0) and is translated by (1, 1) three times, what are the final coordinates?
23. Translate the rectangle with corners (2, 1), (2, 4), (5, 1), and (5, 4) by (-1, 2). What are the new coordinates?
24. What would be the new position of point (4, 4) after translating it twice by (2, -1)?
25. If you translate (3, 3) by (2, 2) and then by (-1, -1), where do you end up?
26. Translate the point (5, 5) by (0, 0). What are the coordinates after translation?
27. If a point at (10, 10) is translated by (-5, -5), what are the new coordinates?
28. Translate the square with vertices (1, 1), (1, 2), (2, 1), and (2, 2) using the vector (3, 3). What are the new vertices?
29. What are the new coordinates of (2, 2) after a translation of (-2, -2) and then (1, 1)?
30. If you have a point at (7, 8) and you translate it by (-5, -3), where will it be?

Answers

Easy Level Answers

1. (3, 4)
2. (4, 2)
3. (5, 2)
4. (2, 3)
5. (4, 2)
6. (4, 3)
7. (4, 5)
8. (3, 2)
9. (2, 3)
10. (3, 3)

Medium Level Answers

11. (5, 3)
12. (3, 5)
13. (2, 5)
14. (4, -4)
15. (5, 7)
16. (2, 6)
17. (3, -2)
18. (4, 6)
19. (5, 5)
20. (4, 3)

Hard Level Answers

21. A(3, 3), B(3, 5), C(6, 3)
22. (3, 3)
23. (1, 3), (1, 6), (4, 3), (4, 6)
24. (9, 3)
25. (4, 4)
26. (5, 5)
27. (5, 5)
28. (4, 4), (4, 5), (5, 4), (5, 5)
29. (1, 1)
30. (2, 5)

I hope this helps you understand translation on a co-ordinate grid better! Now, let’s practice those questions!