Transformations Worksheets (Geometry) | Cazoom Maths - Free Printable

To solve this problem, we need to find the column vector that describes how Shape A moves to its new position in each numbered box.

A column vector is written like this:
$$ \begin{pmatrix} x \\ y \end{pmatrix} $$
- The top number (x) tells us how many squares we move left or right.
- Positive (+) means move right.
- Negative (-) means move left.
- The bottom number (y) tells us how many squares we move up or down.
- Positive (+) means move up.
- Negative (-) means move down.

Let’s go step by step for each shape:

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Problem 1:
Shape A is the grey rectangle. It moves to the orange rectangle.
- Count horizontal movement: From grey to orange is 3 squares to the right → +3
- Count vertical movement: No up or down movement → 0
→ Vector: $\begin{pmatrix} 3 \\ 0 \end{pmatrix}$

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Problem 2:
Shape A is the grey rectangle on top. It moves to the orange rectangle below.
- Horizontal: No left/right movement → 0
- Vertical: Moves 4 squares down → -4
→ Vector: $\begin{pmatrix} 0 \\ -4 \end{pmatrix}$

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Problem 3:
Shape A is the grey rectangle on top right. It moves to the orange rectangle below and left.
- Horizontal: Moves 2 squares left → -2
- Vertical: Moves 4 squares down → -4
→ Vector: $\begin{pmatrix} -2 \\ -4 \end{pmatrix}$

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Problem 4:
Shape A is the grey rectangle on the left. It moves to the blue rectangle on the right.
- Horizontal: Moves 5 squares right → +5
- Vertical: Moves 2 squares up → +2
→ Vector: $\begin{pmatrix} 5 \\ 2 \end{pmatrix}$

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Problem 5:
Shape A is the grey diamond. It moves to the blue diamond on the left.
- Horizontal: Moves 3 squares left → -3
- Vertical: Moves 2 squares up → +2
→ Vector: $\begin{pmatrix} -3 \\ 2 \end{pmatrix}$

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Problem 6:
Shape A is the grey L-shape on the left. It moves to the blue L-shape on the right and down.
- Horizontal: Moves 4 squares right → +4
- Vertical: Moves 3 squares down → -3
→ Vector: $\begin{pmatrix} 4 \\ -3 \end{pmatrix}$

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Problem 7:
Shape A is the grey triangle at the bottom. It moves to the green triangle above and left.
- Horizontal: Moves 2 squares left → -2
- Vertical: Moves 6 squares up → +6
→ Vector: $\begin{pmatrix} -2 \\ 6 \end{pmatrix}$

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Problem 8:
Shape A is the grey star. It moves to the green star on the right.
- Horizontal: Moves 3 squares right → +3
- Vertical: Moves 1 square up → +1
→ Vector: $\begin{pmatrix} 3 \\ 1 \end{pmatrix}$

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Problem 9:
Shape A is the grey square. It moves to the green quarter-circle on the right and down.
- Horizontal: Moves 5 squares right → +5
- Vertical: Moves 4 squares down → -4
→ Vector: $\begin{pmatrix} 5 \\ -4 \end{pmatrix}$

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Final Answer:
1) $\begin{pmatrix} 3 \\ 0 \end{pmatrix}$
2) $\begin{pmatrix} 0 \\ -4 \end{pmatrix}$
3) $\begin{pmatrix} -2 \\ -4 \end{pmatrix}$
4) $\begin{pmatrix} 5 \\ 2 \end{pmatrix}$
5) $\begin{pmatrix} -3 \\ 2 \end{pmatrix}$
6) $\begin{pmatrix} 4 \\ -3 \end{pmatrix}$
7) $\begin{pmatrix} -2 \\ 6 \end{pmatrix}$
8) $\begin{pmatrix} 3 \\ 1 \end{pmatrix}$
9) $\begin{pmatrix} 5 \\ -4 \end{pmatrix}$