Math Problem Statement

What is the image of left parenthesis, minus, 1, comma, minus, 6, right parenthesis(−1,−6) after a reflection over the y-axis?

Solution

To find the image of a point (1,6)(-1, -6) after a reflection over the yy-axis, we follow this rule:

  1. Reflection over the yy-axis: The xx-coordinate changes its sign, while the yy-coordinate remains unchanged.

Given (1,6)(-1, -6):

  • The xx-coordinate, 1-1, becomes 11.
  • The yy-coordinate, 6-6, remains 6-6.

Thus, the reflected point is (1,6)(1, -6).


Do you want a detailed explanation of reflections? Let me know!

Related Questions:

  1. What is the reflection of (3,5)(3, 5) over the yy-axis?
  2. How would you reflect (1,6)(-1, -6) over the xx-axis instead?
  3. What would be the image of (1,6)(-1, -6) after a reflection over the line x=0x = 0?
  4. How do you reflect a point over the origin?
  5. What happens when you reflect a point over the line y=xy = x?

Tip:

When reflecting over the yy-axis, always remember: only the xx-coordinate changes its sign!

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Math Problem Analysis

Mathematical Concepts

Reflection
Coordinate Geometry

Formulas

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

Theorems

Coordinate reflection rules in a Cartesian plane

Suitable Grade Level

Grades 6-8