Math Problem Statement

Draw the reflection of the figure in the y-axis.

Solution

To reflect the given figure over the y-axis, follow these steps:

  1. Identify Points: First, note the coordinates of each vertex of the figure on the right side of the y-axis. Let's assume these points are labeled approximately as follows:

    • Point A (1,1)
    • Point B (3,2)
    • Point C (4,-1)
  2. Reflect Each Point Across the y-Axis: For a reflection over the y-axis, change the sign of the x-coordinate for each point. This gives:

    • A' (-1,1)
    • B' (-3,2)
    • C' (-4,-1)
  3. Plot the New Points: On the left side of the y-axis, plot these reflected points (A', B', C').

  4. Connect the Points: Draw lines connecting A' to B', B' to C', and C' back to A' to complete the reflection of the shape.

Would you like a more detailed explanation or have any specific questions?

Here are five related questions:

  1. How would the reflection change if we reflected over the x-axis instead?
  2. What would happen if we reflected the figure over both the x-axis and y-axis?
  3. How can we determine the reflection of a figure without plotting?
  4. What are some practical applications of geometric reflections?
  5. How would reflecting over a line other than the y-axis affect the coordinates?

Tip: Reflecting over the y-axis only affects the x-coordinates of points, while reflecting over the x-axis only affects the y-coordinates.

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Math Problem Analysis

Mathematical Concepts

Geometry
Transformations
Reflections

Formulas

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

Theorems

Line symmetry
Reflection properties

Suitable Grade Level

Grades 6-8