Solved examples: Translating shapes on a coordinate grid Grade 4

🧭 Understanding Translations

• 📍 A translation is when you slide a shape without rotating or flipping it.
• 📈 You can describe a translation by how many units it moves left or right, and up or down.
• ➕ When translating on a coordinate grid, you add or subtract from the x and y coordinates.
• 📐 If you move a point (x, y) right by 'a' units and up by 'b' units, the new point is (x + a, y + b).

✍️ Examples

• ✨ Example 1: Translate a point (2, 3) right by 4 units and down by 1 unit. New point: (2 + 4, 3 - 1) = (6, 2).
• 💡 Example 2: Translate a square with vertices (1, 1), (1, 2), (2, 1), and (2, 2) left by 2 units and up by 3 units.
  • New vertices: (-1, 4), (-1, 5), (0, 4), and (0, 5).

🧮 Practice Questions

1. A triangle has vertices at (1, 1), (1, 4), and (3, 1). If it is translated 2 units to the right, what are the new coordinates of the vertices?
   1. (3, 3), (3, 6), (5, 3)
   2. (3, 1), (3, 4), (5, 1)
   3. (1, 3), (1, 6), (3, 3)
   4. (-1, 1), (-1, 4), (1, 1)
2. If a point at (5, 2) is translated 3 units down, what are the new coordinates?
   1. (5, 5)
   2. (2, 2)
   3. (5, -1)
   4. (5, 1)
3. A rectangle has vertices at (0, 0), (0, 3), (2, 0), and (2, 3). If it's translated 1 unit left and 2 units up, what are the new vertices?
   1. (1, 2), (1, 5), (3, 2), (3, 5)
   2. (-1, 2), (-1, 5), (1, 2), (1, 5)
   3. (1, -2), (1, 1), (3, -2), (3, 1)
   4. (-1, -2), (-1, 1), (1, -2), (1, 1)
4. What translation moves the point (1, 5) to (4, 7)?
   1. 3 units right, 2 units down
   2. 2 units right, 3 units up
   3. 3 units right, 2 units up
   4. 2 units right, 3 units down
5. A square with one vertex at (2, 2) is translated so that the vertex is now at (5, 5). What translation was applied?
   1. 3 units left, 3 units down
   2. 3 units right, 3 units down
   3. 3 units left, 3 units up
   4. 3 units right, 3 units up
6. If you translate a shape 4 units to the left, what happens to the x-coordinate of each point?
   1. It increases by 4
   2. It stays the same
   3. It decreases by 4
   4. It becomes 4
7. A point is translated from (6, 8) to (10, 5). Describe the translation.
   1. 4 units left, 3 units up
   2. 4 units right, 3 units up
   3. 4 units left, 3 units down
   4. 4 units right, 3 units down