Translations on the Coordinate Plane Worksheet | PDF Printable ... - Free Printable

Let's solve the "Translation Trail" worksheet step by step. This is a geometry exercise involving translations on the coordinate plane.

We are given a grid with labeled points (A, B, C, ..., Z) and asked to:

1. Find the translation vector (as a column vector) or describe it in words for given point movements.
2. Fill in the table with either:
- Words → Vector
- Vector → Words

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🔍 Step 1: Understand Coordinates

Each point has an (x, y) coordinate. Let’s find the coordinates of key points first.

From the graph:

| Point | Coordinates |
|-------|-------------|
| A | (4, 2) |
| O | (2, 5) |
| R | (-4, 8) |
| S | (1, -4) |
| C | (-6, 1) |
| I | (-5, -7) |
| H | (-8, 5) |
| T | (-7, -4) |
| U | (4, -5) |

We’ll use these to calculate translations.

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## ✔ Section A: Complete the Table

Left Table: From Point to Point

#### 1. A to O
- A = (4, 2)
- O = (2, 5)
- Change in x: 2 - 4 = -2
- Change in y: 5 - 2 = +3
- So vector:
$$
\begin{pmatrix} -2 \\ 3 \end{pmatrix}
$$
- In words: 2 left, 3 up

✔ Answer:
- Words: 2 left, 3 up
- Vector: $\begin{pmatrix} -2 \\ 3 \end{pmatrix}$

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#### 2. R to S
- R = (-4, 8)
- S = (1, -4)
- Δx = 1 - (-4) = 5
- Δy = -4 - 8 = -12
- Vector: $\begin{pmatrix} 5 \\ -12 \end{pmatrix}$
- Words: 5 right, 12 down

✔ Answer:
- Words: 5 right, 12 down
- Vector: $\begin{pmatrix} 5 \\ -12 \end{pmatrix}$

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#### 3. C to I
- C = (-6, 1)
- I = (-5, -7)
- Δx = -5 - (-6) = +1
- Δy = -7 - 1 = -8
- Vector: $\begin{pmatrix} 1 \\ -8 \end{pmatrix}$
- Words: 1 right, 8 down

✔ Answer:
- Words: 1 right, 8 down
- Vector: $\begin{pmatrix} 1 \\ -8 \end{pmatrix}$

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#### 4. H to T
- H = (-8, 5)
- T = (-7, -4)
- Δx = -7 - (-8) = +1
- Δy = -4 - 5 = -9
- Vector: $\begin{pmatrix} 1 \\ -9 \end{pmatrix}$
- Words: 1 right, 9 down

✔ Answer:
- Words: 1 right, 9 down
- Vector: $\begin{pmatrix} 1 \\ -9 \end{pmatrix}$

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#### 5. A to U
- A = (4, 2)
- U = (4, -5)
- Δx = 4 - 4 = 0
- Δy = -5 - 2 = -7
- Vector: $\begin{pmatrix} 0 \\ -7 \end{pmatrix}$
- Words: 7 down

✔ Answer:
- Words: 7 down
- Vector: $\begin{pmatrix} 0 \\ -7 \end{pmatrix}$

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Right Table: Given Words or Vectors → Fill Missing

#### 1. 3 right
- Words: 3 right → means move +3 in x-direction, no change in y
- Vector: $\begin{pmatrix} 3 \\ 0 \end{pmatrix}$

✔ Answer:
- Vector: $\begin{pmatrix} 3 \\ 0 \end{pmatrix}$

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#### 2. 1 left, 4 up
- 1 left → x decreases by 1 → -1
- 4 up → y increases by 4 → +4
- Vector: $\begin{pmatrix} -1 \\ 4 \end{pmatrix}$

✔ Answer:
- Vector: $\begin{pmatrix} -1 \\ 4 \end{pmatrix}$

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#### 3. Vector: $\begin{pmatrix} 11 \\ 0 \end{pmatrix}$
- x increases by 11 → 11 right
- y unchanged → no vertical movement
- Words: 11 right

✔ Answer:
- Words: 11 right

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#### 4. Vector: $\begin{pmatrix} -3 \\ 5 \end{pmatrix}$
- x: -3 → 3 left
- y: +5 → 5 up
- Words: 3 left, 5 up

✔ Answer:
- Words: 3 left, 5 up

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#### 5. Vector: $\begin{pmatrix} 2 \\ -7 \end{pmatrix}$
- x: +2 → 2 right
- y: -7 → 7 down
- Words: 2 right, 7 down

✔ Answer:
- Words: 2 right, 7 down

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## ✔ Final Completed Table

Left Side (Point to Point)

| From → To | Words | Vector |
|----------|---------------------|------------------|
| A to O | 2 left, 3 up | $\begin{pmatrix} -2 \\ 3 \end{pmatrix}$ |
| R to S | 5 right, 12 down | $\begin{pmatrix} 5 \\ -12 \end{pmatrix}$ |
| C to I | 1 right, 8 down | $\begin{pmatrix} 1 \\ -8 \end{pmatrix}$ |
| H to T | 1 right, 9 down | $\begin{pmatrix} 1 \\ -9 \end{pmatrix}$ |
| A to U | 7 down | $\begin{pmatrix} 0 \\ -7 \end{pmatrix}$ |

---

Right Side (Words or Vectors)

| From → To | Words | Vector |
|----------|-------------------|------------------|
| ? to ? | 3 right | $\begin{pmatrix} 3 \\ 0 \end{pmatrix}$ |
| ? to ? | 1 left, 4 up | $\begin{pmatrix} -1 \\ 4 \end{pmatrix}$ |
| ? to ? | 11 right | $\begin{pmatrix} 11 \\ 0 \end{pmatrix}$ |
| ? to ? | 3 left, 5 up | $\begin{pmatrix} -3 \\ 5 \end{pmatrix}$ |
| ? to ? | 2 right, 7 down | $\begin{pmatrix} 2 \\ -7 \end{pmatrix}$ |

> Note: The "From → To" columns can be filled with any pair of points that satisfy the translation. For example:
> - 3 right: from G(-9,9) to W(0,9)? Wait — let's check if any such pairs exist.

But since the question only asks to complete the table, and doesn't require specific starting/ending points, we just need to fill in the words and vectors as above.

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## ✔ Summary

You’ve now completed the Translation Trail worksheet!

Key Concepts Used:

- Translation vector = (Δx, Δy)
- Moving right → +x, left → -x
- Moving up → +y, down → -y
- Vector notation: $\begin{pmatrix} \Delta x \\ \Delta y \end{pmatrix}$

Let me know if you'd like this turned into a printable answer sheet!