Which algebraic representation explains the effect of the transformation from△
ABC to △
A'B'C'?
A.open parentheses x comma y close parentheses rightwards arrow open parentheses x minus 2 comma space y plus 5 close parentheses, because the pre-image is translated two units to the left and five units up.
B.open parentheses x comma y close parentheses rightwards arrow open parentheses x plus 2 comma space y minus 5 close parentheses, because the pre-image is translated two units to the right and five units down.
C.open parentheses x comma y close parentheses rightwards arrow left parenthesis x minus 5 comma space y plus 2 right parenthesis, because the pre-image is translated five units to the left and two units up.
D.open parentheses x comma y close parentheses rightwards arrow left parenthesis x plus 5 comma space y minus 2 right parenthesis, because the pre-image is translated five units to the right and two units down.

The correct answer is:

**A. (x, y) → (x - 2, y + 5), because the pre-image is translated two units to the left and five units up.**

Here's the reasoning:

- **Translation** involves moving every point of a shape in the same direction by the same distance. This can be represented algebraically by adding or subtracting values to the x and y coordinates.

- The expression \((x, y) \rightarrow (x - 2, y + 5)\) means:
  - The x-coordinate is adjusted by subtracting 2, which translates the shape 2 units to the left.
  - The y-coordinate is adjusted by adding 5, which translates the shape 5 units up.

Given this understanding, option A correctly describes the transformation that translates the pre-image (triangle \( \triangle ABC \)) 2 units to the left and 5 units up to create the image (\(\triangle A'B'C'\)). 

Do you want further details or have any questions? Here are some related questions you might find useful:

1. How do other transformations, such as reflections or rotations, affect coordinates?
2. What is the effect of a translation of \((x, y) \rightarrow (x + a, y + b)\)?
3. How can you identify transformations on a coordinate plane?
4. What is the difference between rigid and non-rigid transformations?
5. How do you determine the line of symmetry for a reflection transformation?

**Tip:** For translations, remember that adding to x moves right, subtracting from x moves left, adding to y moves up, and subtracting from y moves down.

Which algebraic representation explains the effect of the transformation from △ABC to △A'B'C'? A. (x, y) → (x - 2, y + 5), because the pre-image is translated two units to the left and five units up. B. (x, y) → (x + 2, y - 5), because the pre-image is translated two units to the right and five units down. C. (x, y) → (x - 5, y + 2), because the pre-image is translated five units to the left and two units up. D. (x, y) → (x + 5, y - 2), because the pre-image is translated five units to the right and two units down.

Explore how to solve the problem of translating triangle △ABC to △A'B'C' using algebraic representation. This problem involves translating points in coordinate geometry and is suitable for students in Grades 7-9.

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