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

Explanation:
Let’s solve each part step by step.

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Part 1: Slide 8 left and 5 down

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

A *slide* (translation) means we move every point the same amount horizontally and vertically.

- “8 left” means subtract 8 from the x-coordinate.
- “5 down” means subtract 5 from the y-coordinate.

So apply:
(x, y) → (x − 8, y − 5)

Compute new points:

- A′ = (−6 − 8, −2 − 5) = (−14, −7)
- B′ = (−4 − 8, −2 − 5) = (−12, −7)
- C′ = (−6 − 8, −6 − 5) = (−14, −11)

Label these on the grid as A′, B′, C′.

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Part 2: Transformation (x, y) → (x + 8, y + 3)

Given pre-image points:
A(−6, −2), B(−4, −2), C(−6, −6)

Apply rule: add 8 to x, add 3 to y.

- A″ = (−6 + 8, −2 + 3) = (2, 1)
- B″ = (−4 + 8, −2 + 3) = (4, 1)
- C″ = (−6 + 8, −6 + 3) = (2, −3)

Label these as A″, B″, C″.

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Part 3a: Polygon P(4, 0), Q(2, 0), R(2, 3), S(4, 3)
Transformation: (x, y) → (x + 4, y − 5)

Compute image points:

- P′ = (4 + 4, 0 − 5) = (8, −5)
- Q′ = (2 + 4, 0 − 5) = (6, −5)
- R′ = (2 + 4, 3 − 5) = (6, −2)
- S′ = (4 + 4, 3 − 5) = (8, −2)

Plot and label P′, Q′, R′, S′.

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Part 3b: Polygon A(0, 0), B(−4, 0), C(−4, 3), D(0, 3)
Transformation: (x, y) → (x + 6, y + 2)

Compute image:

- A′ = (0 + 6, 0 + 2) = (6, 2)
- B′ = (−4 + 6, 0 + 2) = (2, 2)
- C′ = (−4 + 6, 3 + 2) = (2, 5)
- D′ = (0 + 6, 3 + 2) = (6, 5)

Plot and label A′, B′, C′, D′.

All transformations are just moving points using the given rules — no rotation or reflection, just sliding.

Final Answer:
For part 1: A′(−14, −7), B′(−12, −7), C′(−14, −11)
For part 2: A″(2, 1), B″(4, 1), C″(2, −3)
For part 3a: P′(8, −5), Q′(6, −5), R′(6, −2), S′(8, −2)
For part 3b: A′(6, 2), B′(2, 2), C′(2, 5), D′(6, 5)