Math Problem Statement

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

Translate \( \triangle ABC \) according to the translation rule \( (x, y) \rightarrow (x + 4, y - 3) \). List the coordinates of the new triangle \( \triangle A'B'C' \).

Solution

To apply the translation (x,y)(x+4,y3)(x, y) \rightarrow (x + 4, y - 3) to each point of ABC\triangle ABC, let's calculate the new coordinates:

  1. Point A(5,2)A(-5, 2): A=(5+4,23)=(1,1)A' = (-5 + 4, 2 - 3) = (-1, -1)

  2. Point B(3,4)B(-3, 4): B=(3+4,43)=(1,1)B' = (-3 + 4, 4 - 3) = (1, 1)

  3. Point C(2,0)C(-2, 0): C=(2+4,03)=(2,3)C' = (-2 + 4, 0 - 3) = (2, -3)

The coordinates of the new triangle ABC\triangle A'B'C' are:

  • A=(1,1)A' = (-1, -1)
  • B=(1,1)B' = (1, 1)
  • C=(2,3)C' = (2, -3)

Would you like to delve deeper into translation transformations or have any questions?

Here are five related questions to explore further:

  1. How does translating a figure affect its orientation and size?
  2. What are some real-world applications of geometric translations?
  3. How would the triangle’s position change with different translation vectors?
  4. Can you describe the transformation if we reversed the translation direction?
  5. What other transformations besides translation could be applied to ABC\triangle ABC?

Tip: Visualizing transformations on a graph helps solidify understanding of coordinate changes.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Translation

Formulas

(x, y) → (x + a, y + b) for translation by vector (a, b)

Theorems

Translation transformation

Suitable Grade Level

Grades 6-8