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

Problem Analysis:

The worksheet involves translations of geometric figures on a coordinate grid. Translation means moving a figure to a new position without changing its size, shape, or orientation. The task requires us to translate given points and then determine the new coordinates after the translation.

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Section 1: Practice Problems

#### Problem 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 and 2 units up.
- Moving right increases the x-coordinate by 7.
- Moving up increases the y-coordinate by 2.

- New Coordinates Calculation:
- 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)

- Final Answer for Problem 1:
- A'(-1, 4)
- B'(3, 4)
- C'(4, 0)
- D'(-1, 0)

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#### Problem 2:
Translate figure ABCD using the rule \((x - 5, y - 10)\).
- Original Coordinates:
- A(3, 4)
- B(6, 6)
- C(9, 4)
- D(6, 2)

- Translation Rule: Subtract 5 from the \(x\)-coordinate and subtract 10 from the \(y\)-coordinate.

- New Coordinates Calculation:
- 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)

- Final Answer for Problem 2:
- A'(-2, -6)
- B'(1, -4)
- C'(4, -6)
- D'(1, -8)

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Section 2: Practice Problems

#### Problem 1:
Graph the figure with the given points, then translate using the rule \((x + 4, y + 3)\).
- Original Coordinates:
- A(-4, -1)
- B(-5, -5)
- C(-3, -2)

- Translation Rule: Add 4 to the \(x\)-coordinate and add 3 to the \(y\)-coordinate.

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

- Final Answer for Problem 1:
- A'(0, 2)
- B'(-1, -2)
- C'(1, 1)

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#### Problem 2:
Graph the figure with the given points, then translate using the rule \((x + 6, y - 12)\).
- Original Coordinates:
- A(-8, 6)
- B(-9, 9)
- C(-4, 5)
- D(-1, 2)

- Translation Rule: Add 6 to the \(x\)-coordinate and subtract 12 from the \(y\)-coordinate.

- New Coordinates Calculation:
- 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)

- Final Answer for Problem 2:
- A'(-2, -6)
- B'(-3, -3)
- C'(2, -7)
- D'(5, -10)

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Final Answers:

1. Problem 1 (Section 1):
- A'(-1, 4)
- B'(3, 4)
- C'(4, 0)
- D'(-1, 0)

2. Problem 2 (Section 1):
- A'(-2, -6)
- B'(1, -4)
- C'(4, -6)
- D'(1, -8)

3. Problem 1 (Section 2):
- A'(0, 2)
- B'(-1, -2)
- C'(1, 1)

4. Problem 2 (Section 2):
- A'(-2, -6)
- B'(-3, -3)
- C'(2, -7)
- D'(5, -10)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Section 1:} \\
1. \text{A'}(-1, 4), \text{B'}(3, 4), \text{C'}(4, 0), \text{D'}(-1, 0) \\
2. \text{A'}(-2, -6), \text{B'}(1, -4), \text{C'}(4, -6), \text{D'}(1, -8) \\
\text{Section 2:} \\
1. \text{A'}(0, 2), \text{B'}(-1, -2), \text{C'}(1, 1) \\
2. \text{A'}(-2, -6), \text{B'}(-3, -3), \text{C'}(2, -7), \text{D'}(5, -10)
\end{array}
}
\]