Translation Worksheet Answer Key - Fill Online, Printable ... - Free Printable

Let's solve each problem step by step from the Translations Worksheet you provided.

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Problem 1:

> Slide 8 left and 5 down.

We are given a triangle with vertices:
- A(4, 6)
- B(6, 2)
- C(2, 2)

We need to translate this triangle 8 units left (subtract 8 from x) and 5 units down (subtract 5 from y).

#### Step-by-step translation:
- A(4, 6) → (4 - 8, 6 - 5) = (-4, 1)
- B(6, 2) → (6 - 8, 2 - 5) = (-2, -3)
- C(2, 2) → (2 - 8, 2 - 5) = (-6, -3)

#### Final Image Vertices:
- A'(-4, 1)
- B'(-2, -3)
- C'(-6, -3)

✔ Plot these points on the grid and draw the translated triangle. Label the image as A'B'C'.

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Problem 2:

> Translate using vector: (x, y) → (x + 8, y + 10)

Given quadrilateral with vertices:
- A(-4, -1)
- B(-4, -7)
- C(-6, -6)
- D(-6, -1)

Apply transformation: Add 8 to x, add 10 to y

#### Translated points:
- A(-4, -1) → (-4 + 8, -1 + 10) = (4, 9)
- B(-4, -7) → (-4 + 8, -7 + 10) = (4, 3)
- C(-6, -6) → (-6 + 8, -6 + 10) = (2, 4)
- D(-6, -1) → (-6 + 8, -1 + 10) = (2, 9)

#### Final Image Vertices:
- A'(4, 9)
- B'(4, 3)
- C'(2, 4)
- D'(2, 9)

✔ Plot these points and draw the new quadrilateral. Label it A'B'C'D'.

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Problem 3a:

> Graph and label the polygon determined by the coordinates below, then graph and label the image created by the transformation:

Original Points:
- P(4, 3)
- Q(7, 3)
- R(5, 7)

Transformation:
(x, y) → (x + 4, y – 5)

#### Apply transformation:
- P(4, 3) → (4+4, 3–5) = (8, -2)
- Q(7, 3) → (7+4, 3–5) = (11, -2)
- R(5, 7) → (5+4, 7–5) = (9, 2)

#### New Points:
- P'(8, -2)
- Q'(11, -2)
- R'(9, 2)

✔ Graph the original triangle PQR and the image triangle P'Q'R'.

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Problem 3b:

> Original Points:
- A(0, 0)
- B(-4, 0)
- C(-4, 3)

Transformation:
(x, y) → (x + 6, y + 2)

#### Apply transformation:
- A(0, 0) → (0+6, 0+2) = (6, 2)
- B(-4, 0) → (-4+6, 0+2) = (2, 2)
- C(-4, 3) → (-4+6, 3+2) = (2, 5)

#### New Points:
- A'(6, 2)
- B'(2, 2)
- C'(2, 5)

✔ Graph the original triangle ABC and the image triangle A'B'C'.

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✔ Summary of Answers:

| Problem | Original Points | Transformation | Image Points |
|--------|------------------|----------------|---------------|
| 1 | A(4,6), B(6,2), C(2,2) | (x−8, y−5) | A'(-4,1), B'(-2,-3), C'(-6,-3) |
| 2 | A(-4,-1), B(-4,-7), C(-6,-6), D(-6,-1) | (x+8, y+10) | A'(4,9), B'(4,3), C'(2,4), D'(2,9) |
| 3a | P(4,3), Q(7,3), R(5,7) | (x+4, y−5) | P'(8,-2), Q'(11,-2), R'(9,2) |
| 3b | A(0,0), B(-4,0), C(-4,3) | (x+6, y+2) | A'(6,2), B'(2,2), C'(2,5) |

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🔍 How to Graph:

1. Use the coordinate grid.
2. Plot the original points and connect them to form the shape.
3. Plot the transformed points.
4. Connect the new points in the same order.
5. Label all vertices clearly (e.g., A, B, C for pre-image; A', B', C' for image).
6. Optionally, use arrows to show direction of translation.

Let me know if you'd like me to generate a visual version or help you plot it!