Math Problem Statement

Triangle ABC is transformed to form triangle A'B'C'. A is at (3, 1), B is at (1, 8), and C is at (7, 2). Which transformation happened to triangle ABC to form A'B'C'?

Solution

The problem involves a transformation of triangle ABC\triangle ABC into ABC\triangle A'B'C' on the coordinate plane.

Given Points:

  • A(3,1)A(3, 1)
  • B(1,8)B(1, 8)
  • C(7,2)C(7, 2)

Transformation Analysis:

To identify the transformation, let's compare the positions of the original triangle ABC\triangle ABC and the image ABC\triangle A'B'C'. Observing the transformation visually, it looks like the triangle has been reflected.

Transformation Identification:

  • The triangle ABC\triangle ABC has been reflected across the x-axis to form ABC\triangle A'B'C'.

Conclusion: The transformation statement is: ABC is reflected across the x-axis to form ABC.\triangle ABC \text{ is reflected across the x-axis to form } \triangle A'B'C'.

Do you want more details or have any questions?

Related Questions:

  1. What are the coordinates of AA', BB', and CC' after the transformation?
  2. How can you determine a reflection over the y-axis instead of the x-axis?
  3. What would be the result if the triangle were rotated 90° about the origin?
  4. How do you verify a dilation transformation on a coordinate plane?
  5. What are the effects of translating a triangle 4 units left and 3 units up?

Tip:

To verify reflections, check if each point is equidistant from the axis of reflection and lies on the opposite side of that axis.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Transformations
Reflections
Coordinate Geometry

Formulas

-

Theorems

Reflection Theorem

Suitable Grade Level

Grades 8-10