Year 10 Transformations Worksheets | PDF Printable Worksheets - Free Printable

Let’s solve each problem step by step.

We are given shapes on a grid. Shape A is the original (gray). The colored shape is the translated version. We need to find the column vector that describes how to move from shape A to the new shape.

A column vector looks like this:
```
( x )
( y )
```
- x = horizontal movement (right is positive, left is negative)
- y = vertical movement (up is positive, down is negative)

We’ll pick one point on shape A (like the top-left corner) and see where it moves to on the new shape. Then we count how many squares right/left and up/down.

---

Problem 1:
Shape A is gray rectangle at left. Orange rectangle is to its right.
Pick top-left corner of A: let’s say it’s at (2,5) — but we don’t need exact coords, just count steps.
From A to orange: move 3 squares right, 0 up/down.
→ Vector:
```
( 3 )
( 0 )
```

Problem 2:
Gray A is above, orange is below.
Move from A to orange: 0 left/right, 4 down → so y = -4
→ Vector:
```
( 0 )
(-4 )
```

Problem 3:
Gray A is above, orange is directly below it.
Count: same column, moved down 3 squares.
→ Vector:
```
( 0 )
(-3 )
```

Problem 4:
Gray A is bottom-left, blue rectangle is top-right.
From A to blue: move 4 right, 2 up
→ Vector:
```
( 4 )
( 2 )
```

Problem 5:
Gray diamond A is left, gray diamond B is right and slightly down.
From A to B: move 3 right, 2 down → y = -2
→ Vector:
```
( 3 )
(-2 )
```

Problem 6:
Gray L-shape A is top-left, blue L-shape is bottom-right.
From A to blue: move 3 right, 2 down
→ Vector:
```
( 3 )
(-2 )
```

Problem 7:
Green triangle A is left, gray triangle is right and lower.
From green to gray: move 3 right, 4 down
→ Vector:
```
( 3 )
(-4 )
```

Problem 8:
Gray star A is left, green star is right and slightly down.
From A to green: move 3 right, 1 down
→ Vector:
```
( 3 )
(-1 )
```

Problem 9:
Gray shape A is top-left, green shape is bottom-right.
From A to green: move 4 right, 3 down
→ Vector:
```
( 4 )
(-3 )
```

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Final Answer:
1) ( 3 )
( 0 )

2) ( 0 )
(-4 )

3) ( 0 )
(-3 )

4) ( 4 )
( 2 )

5) ( 3 )
(-2 )

6) ( 3 )
(-2 )

7) ( 3 )
(-4 )

8) ( 3 )
(-1 )

9) ( 4 )
(-3 )