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

Problem Analysis:

The worksheet involves translations of geometric figures on a coordinate grid. Translations are transformations that move every point of a figure the same distance in the same direction. The task requires us to:
1. Translate given points according to specified rules.
2. List the new coordinates after the translation.

Solution:

#### 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: Add 7 to the x-coordinate.
- Move 2 units up: Add 2 to the y-coordinate.

- New Coordinates:
- 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)

##### 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.
- Subtract 10 from the y-coordinate.

- New Coordinates:
- 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 points A(-4, -1), B(-5, -5), C(-3, -2), 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.
- Add 3 to the y-coordinate.

- New Coordinates:
- 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)

##### Problem 2:
Graph the figure with points A(-8, 6), B(-9, 9), C(-4, 5), D(-1, 2), 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.
- Subtract 12 from the y-coordinate.

- New Coordinates:
- 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)

Boxed Final Answer:

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