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 All 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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📌 Instructions for Graphing:

1. Use graph paper or coordinate plane.
2. Plot the original points and connect them to form the pre-image.
3. Plot the translated points and connect them to form the image.
4. Label all vertices clearly (e.g., A, B, C and A', B', C').
5. Optionally, use arrows to show direction of translation.

Let me know if you'd like a visual sketch or explanation of how translations work!