Math Problem Statement

The triangle ABC has been translated into triangle A'B'C' on a grid. Describe the transformation that has taken place.

Solution

The problem asks to describe the transformation of triangle ABCABC to triangle ABCA'B'C'. Based on the image provided:

  • The transformation appears to be a translation. We can verify this by comparing the coordinates of corresponding points.
  • AA moves to AA', BB moves to BB', and CC remains stationary. Looking at the grid, the points AA and BB seem to shift to the right.

To confirm the translation, let's analyze the movement of points:

  • Point AA moves from (2,3)(-2, 3) to (0,3)(0, 3), which means it moves 2 units to the right.
  • Point BB moves from (3,1)(-3, 1) to (1,1)(-1, 1), also moving 2 units to the right.

So, the transformation is a translation 2 units to the right.

Would you like further clarification, or do you have any questions about this solution?

Here are 5 related questions:

  1. How can you verify a translation using vector notation?
  2. What other types of transformations could be applied to a triangle?
  3. How would the transformation change if point CC had also moved?
  4. Can you describe the properties of a shape that remain unchanged after a translation?
  5. How do you find the equation of a line passing through two points on a grid?

Tip: When describing a translation, always check if all points move by the same distance and direction to ensure it is not a different transformation, such as a reflection or rotation.

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Math Problem Analysis

Mathematical Concepts

Translation
Coordinate Geometry

Formulas

Translation Formula: (x, y) → (x + a, y + b)

Theorems

Translation Theorem: All points of a figure move the same distance in the same direction.

Suitable Grade Level

Grades 7-9