Math Problem Statement

The shape below is reflected in the y-axis. What are the coordinates of the vertex that B maps to after this reflection?

Solution

The question asks for the coordinates of point BB after the shape is reflected over the yy-axis.

Step-by-step solution:

  1. Coordinates of Point B: The original coordinates of point BB are (2,5)(2, 5).

  2. Reflection Over the yy-axis:

    • When reflecting a point over the yy-axis, the xx-coordinate changes its sign, while the yy-coordinate remains the same.
    • Therefore, the reflection of point (x,y)(x, y) over the yy-axis will be (x,y)(-x, y).
  3. Apply the Reflection:

    • The xx-coordinate of BB is 2, so after reflecting over the yy-axis, it becomes 2-2.
    • The yy-coordinate remains 5.
  4. Result: The new coordinates of the vertex that point BB maps to are (2,5)(-2, 5).

Would you like more details on the reflection process or have any other questions?

Here are five related questions for further practice:

  1. What are the coordinates of the vertex at (1,3)(1, 3) after reflecting over the yy-axis?
  2. How would the shape look if reflected over the xx-axis instead?
  3. What happens to the coordinates if the shape is rotated 180 degrees about the origin?
  4. What are the coordinates of point BB after translating it 3 units to the left?
  5. How would the reflection change if we reflected over the line x=1x = 1?

Tip: When reflecting over the yy-axis, only the sign of the xx-coordinate changes, while the yy-coordinate stays the same.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Reflections

Formulas

Reflection over y-axis: (x, y) → (-x, y)

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-8