Math Problem Statement

Point UU is located at left parenthesis, 6, comma, 3, right parenthesis(6,3) on the coordinate plane. Point UU is reflected over the xx-axis to create point U, primeU ′ . Point U, primeU ′ is then reflected over the yy-axis to create point U, start superscript, prime, prime, end superscriptU ′′ . What ordered pair describes the location of U, start superscript, prime, prime, end superscript, question markU ′′ ?

Solution

Let's break down the problem step by step.

Step 1: Reflect Point U(6,3)U(6, 3) over the xx-axis

  • Reflection over the xx-axis changes the sign of the yy-coordinate, so: U=(6,3)U' = (6, -3)

Step 2: Reflect Point U(6,3)U'(6, -3) over the yy-axis

  • Reflection over the yy-axis changes the sign of the xx-coordinate, so: U=(6,3)U'' = (-6, -3)

Final Answer:

The ordered pair that describes the location of UU'' is (6,3)(-6, -3).

Would you like more details on how reflections work, or do you have any other questions?

Here are some related questions you might find useful:

  1. What are the coordinates of a point after a reflection over the origin?
  2. How do you reflect a point over the line y=xy = x?
  3. What happens when you reflect a point twice over the same axis?
  4. How do you find the midpoint between two reflected points?
  5. What is the general formula for reflecting a point over a given line?

Tip: Remember, reflecting over the xx-axis only affects the yy-coordinate, while reflecting over the yy-axis only affects the xx-coordinate.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Plane
Reflections

Formulas

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

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-8