Math Problem Statement

ΔBCD contains the points: B(2,3) C(2,1) D(5,1). If the triangle is reflected across the x-axis, what will B' be?

Solution

The question asks about reflecting the triangle ΔBCD\Delta BCD across the x-axis. The point BB has the coordinates B(2,3)B(2, 3).

To reflect a point across the x-axis, the rule is that the x-coordinate remains the same, while the y-coordinate changes sign. Therefore, the reflection of B(2,3)B(2, 3) across the x-axis will be B(2,3)B'(2, -3).

Thus, the correct answer is:

B'(2, -3)

Would you like more details on how reflections work in geometry? Here are 5 related questions to explore:

  1. How do you reflect a point across the y-axis?
  2. What happens to a shape when it is reflected across both the x- and y-axis?
  3. Can you explain the reflection of an entire triangle across a line?
  4. What are some common rules for reflecting shapes across the origin?
  5. How do you find the distance between a point and its reflection?

Tip: When reflecting over the x-axis, always remember that only the y-coordinate changes sign!

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Math Problem Analysis

Mathematical Concepts

Geometry
Reflections
Coordinate Systems

Formulas

Reflection across the x-axis: (x, y) -> (x, -y)

Theorems

Reflection Theorem in Geometry

Suitable Grade Level

Grades 6-8