Translation In Math Worksheets, Definition, And Examples - Free Printable

Let’s solve each problem step by step, explaining the translation process.

---

## Section 1: Practice Problems

Problem 1.1: Translate figure ABCD seven units right and two units up.

Original coordinates:
- A(-8, 2)
- B(-4, 2)
- C(-3, -2)
- D(-8, -2)

Translation Rule:
Move 7 units right → add 7 to each x-coordinate.
Move 2 units up → add 2 to each y-coordinate.
So, new point = (x + 7, y + 2)

Apply to each point:

- A' = (-8 + 7, 2 + 2) = (-1, 4)
- B' = (-4 + 7, 2 + 2) = (3, 4)
- C' = (-3 + 7, -2 + 2) = (4, 0)
- D' = (-8 + 7, -2 + 2) = (-1, 0)

✔ New Coordinates:
> A'(-1, 4), B'(3, 4), C'(4, 0), D'(-1, 0)

*(You would plot these on the grid provided — all points shift right 7, up 2.)*

---

Problem 1.2: Translate figure ABCD (x - 5, y - 10)

This means subtract 5 from each x-coordinate and subtract 10 from each y-coordinate.

Original coordinates:
- A(3, 4)
- B(6, 6)
- C(9, 4)
- D(6, 2)

Apply translation (x - 5, y - 10):

- A' = (3 - 5, 4 - 10) = (-2, -6)
- B' = (6 - 5, 6 - 10) = (1, -4)
- C' = (9 - 5, 4 - 10) = (4, -6)
- D' = (6 - 5, 2 - 10) = (1, -8)

✔ New Coordinates:
> A'(-2, -6), B'(1, -4), C'(4, -6), D'(1, -8)

*(Plot these — the whole figure moves left 5, down 10.)*

---

## Section 2: Practice Problems

Problem 2.1: Graph the figure, then translate (x + 4, y + 3)

Original coordinates:
- A(-4, -1)
- B(-5, -5)
- C(-3, -2)

Translation: Add 4 to x, add 3 to y → (x + 4, y + 3)

Compute new points:

- A' = (-4 + 4, -1 + 3) = (0, 2)
- B' = (-5 + 4, -5 + 3) = (-1, -2)
- C' = (-3 + 4, -2 + 3) = (1, 1)

✔ New Coordinates:
> A'(0, 2), B'(-1, -2), C'(1, 1)

*(First, plot A, B, C on the grid. Then plot A', B', C' — shifted right 4, up 3.)*

---

Problem 2.2: Graph the figure, then translate (x + 6, y - 12)

Original coordinates:
- A(-8, 6)
- B(-9, 9)
- C(-4, 5)
- D(-1, 2)

Translation: Add 6 to x, subtract 12 from y → (x + 6, y - 12)

Compute new points:

- A' = (-8 + 6, 6 - 12) = (-2, -6)
- B' = (-9 + 6, 9 - 12) = (-3, -3)
- C' = (-4 + 6, 5 - 12) = (2, -7)
- D' = (-1 + 6, 2 - 12) = (5, -10)

✔ New Coordinates:
> A'(-2, -6), B'(-3, -3), C'(2, -7), D'(5, -10)

*(Plot original points first, then translate — move right 6, down 12.)*

---

## ✔ Final Answers Summary:

Section 1:

1.1 → A'(-1,4), B'(3,4), C'(4,0), D'(-1,0)
1.2 → A'(-2,-6), B'(1,-4), C'(4,-6), D'(1,-8)

Section 2:

2.1 → A'(0,2), B'(-1,-2), C'(1,1)
2.2 → A'(-2,-6), B'(-3,-3), C'(2,-7), D'(5,-10)

---

📌 Key Concept Reminder:
In translations, every point of the figure moves the same distance in the same direction. The rule is applied to each vertex individually.

Let me know if you’d like help graphing them too!