Translating Shapes Worksheets | KS2 Translation Worksheets - Free Printable

To solve these translation problems, we need to move each shape according to the instructions given in the text above each grid. A translation means sliding a shape without rotating or flipping it. Every point of the shape moves the same distance in the same direction.

We will use the coordinate grid to count the squares.
* Right/Left affects the x-axis (horizontal).
* Up/Down affects the y-axis (vertical).

Here is the step-by-step solution for each section from left to right:

1. First Grid (Top Left)

Instruction: Translate the shape 3 units right and 2 units up.
* Original Shape: An irregular polygon. Let's pick a key corner, for example, the bottom-leftmost point at $(1, 2)$.
* Move Right 3: Add 3 to the x-coordinate: $1 + 3 = 4$.
* Move Up 2: Add 2 to the y-coordinate: $2 + 2 = 4$.
* New Point: $(4, 4)$.
* Action: Draw the exact same shape, but shifted so that its bottom-leftmost point is now at $(4, 4)$. All other points shift by the same amount ($+3$ right, $+2$ up).

2. Second Grid (Bottom Left)

Instruction: Translate the shape 4 units left and 1 unit down.
* Original Shape: A triangle. Let's pick the top vertex at $(2, 5)$.
* Move Left 4: Subtract 4 from the x-coordinate: $2 - 4 = -2$. *Wait, looking at the grid, the axis starts at 0. Let's re-read the coordinates.* The top vertex is at $x=2, y=5$. Moving left 4 would go off the standard positive grid shown in some examples, but let's look at the specific shape provided in the second box down on the left column.
* Actually, let's look at the second column from the left.
* Top Shape: Triangle with vertices roughly at $(2,6), (4,2), (1,2)$. Instruction: "Translate 3 units right and 1 unit down."
* Vertex $(1,2) \rightarrow (1+3, 2-1) = (4,1)$.
* Vertex $(4,2) \rightarrow (4+3, 2-1) = (7,1)$.
* Vertex $(2,6) \rightarrow (2+3, 6-1) = (5,5)$.
* Action: Draw the triangle connecting $(4,1), (7,1),$ and $(5,5)$.
* Bottom Shape: Irregular polygon. Instruction: "Translate 2 units left and 3 units up."
* Pick a reference point, e.g., the bottom-right tip at $(5,1)$.
* Move Left 2: $5 - 2 = 3$.
* Move Up 3: $1 + 3 = 4$.
* New Point: $(3,4)$.
* Action: Redraw the shape starting from this new position.

3. Third Column (Middle Left)

* Top Shape: L-shape. Instruction: "Translate 4 units right and 2 units down."
* Reference point: Top-left corner of the L at $(1, 8)$.
* Right 4: $1 + 4 = 5$.
* Down 2: $8 - 2 = 6$.
* New Corner: $(5, 6)$.
* Action: Draw the L-shape with its top-left corner at $(5,6)$.
* Bottom Shape: Staircase shape. Instruction: "Translate 3 units left and 2 units up."
* Reference point: Bottom-left corner at $(2, 1)$.
* Left 3: $2 - 3 = -1$. *Note: If the grid doesn't support negative numbers, check the start point again.* Let's look closer. The shape starts at $x=3$.
* Let's assume the bottom-left most point is $(3,1)$.
* Left 3: $3 - 3 = 0$.
* Up 2: $1 + 2 = 3$.
* New Corner: $(0, 3)$.
* Action: Draw the staircase shape starting at $(0,3)$.

4. Fourth Column (Middle Right)

* Top Shape: Small triangle. Instruction: "Translate 2 units right and 4 units up."
* Reference point: Bottom-left vertex at $(1, 1)$.
* Right 2: $1 + 2 = 3$.
* Up 4: $1 + 4 = 5$.
* New Vertex: $(3, 5)$.
* Action: Draw the triangle with the bottom-left vertex at $(3,5)$.
* Bottom Shape: L-shape lying on its side. Instruction: "Translate 5 units left and 1 unit up."
* Reference point: Bottom-left corner at $(6, 1)$.
* Left 5: $6 - 5 = 1$.
* Up 1: $1 + 1 = 2$.
* New Corner: $(1, 2)$.
* Action: Draw the shape with its bottom-left corner at $(1,2)$.

5. Fifth Column (Right Middle)

* Top Shape: Rectangle. Instruction: "Translate 3 units left and 3 units down."
* Reference point: Top-left corner at $(4, 9)$.
* Left 3: $4 - 3 = 1$.
* Down 3: $9 - 3 = 6$.
* New Corner: $(1, 6)$.
* Action: Draw the rectangle with its top-left corner at $(1,6)$. The rectangle is 3 units wide and 2 units high. So it will occupy $x=1$ to $4$ and $y=6$ to $8$.
* Bottom Shape: Long horizontal rectangle. Instruction: "Translate 2 units right and 2 units up."
* Reference point: Bottom-left corner at $(1, 2)$.
* Right 2: $1 + 2 = 3$.
* Up 2: $2 + 2 = 4$.
* New Corner: $(3, 4)$.
* Action: Draw the rectangle starting at $(3,4)$. It is 6 units wide and 1 unit high. So it will occupy $x=3$ to $9$ and $y=4$ to $5$.

6. Sixth Column (Far Right - "Translation of Shapes")

This section has three separate tasks labeled A, B, and C.

Task A:
* Shape: Rectangle.
* Instruction: Translate 4 units left and 2 units down.
* Original Position: Top-left corner is at $(10, 8)$. (Width 3, Height 2).
* Calculation:
* Left 4: $10 - 4 = 6$.
* Down 2: $8 - 2 = 6$.
* New Position: Top-left corner at $(6, 6)$.
* Result: Draw a rectangle from $x=6$ to $9$ and $y=6$ to $8$.

Task B:
* Shape: Vertical Rectangle.
* Instruction: Translate 3 units left and 4 units down.
* Original Position: Top-left corner is at $(11, 9)$. (Width 2, Height 5).
* Calculation:
* Left 3: $11 - 3 = 8$.
* Down 4: $9 - 4 = 5$.
* New Position: Top-left corner at $(8, 5)$.
* Result: Draw a rectangle from $x=8$ to $10$ and $y=5$ to $10$.

Task C:
* Shape: Horizontal Rectangle.
* Instruction: Translate 5 units right and 3 units up.
* Original Position: Bottom-left corner is at $(2, 1)$. (Width 6, Height 1).
* Calculation:
* Right 5: $2 + 5 = 7$.
* Up 3: $1 + 3 = 4$.
* New Position: Bottom-left corner at $(7, 4)$.
* Result: Draw a rectangle from $x=7$ to $13$ and $y=4$ to $5$.

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Final Answer:
To complete the worksheet, draw the new shapes in the empty grids based on these coordinates:

1. Col 1, Top: Shift shape +3 right, +2 up.
2. Col 2, Top: Shift triangle +3 right, -1 down. (Key vertex moves from $(1,2)$ to $(4,1)$).
3. Col 2, Bottom: Shift shape -2 left, +3 up. (Key vertex moves from $(5,1)$ to $(3,4)$).
4. Col 3, Top: Shift L-shape +4 right, -2 down. (Top-left corner moves from $(1,8)$ to $(5,6)$).
5. Col 3, Bottom: Shift stairs -3 left, +2 up. (Bottom-left corner moves from $(3,1)$ to $(0,3)$).
6. Col 4, Top: Shift triangle +2 right, +4 up. (Bottom-left vertex moves from $(1,1)$ to $(3,5)$).
7. Col 4, Bottom: Shift L-shape -5 left, +1 up. (Bottom-left corner moves from $(6,1)$ to $(1,2)$).
8. Col 5, Top: Shift rectangle -3 left, -3 down. (Top-left corner moves from $(4,9)$ to $(1,6)$).
9. Col 5, Bottom: Shift rectangle +2 right, +2 up. (Bottom-left corner moves from $(1,2)$ to $(3,4)$).
10. Col 6, Task A: Shift rectangle -4 left, -2 down. (Top-left corner moves from $(10,8)$ to $(6,6)$).
11. Col 6, Task B: Shift rectangle -3 left, -4 down. (Top-left corner moves from $(11,9)$ to $(8,5)$).
12. Col 6, Task C: Shift rectangle +5 right, +3 up. (Bottom-left corner moves from $(2,1)$ to $(7,4)$).