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 over the -axis
- Reflection over the -axis changes the sign of the -coordinate, so:
Step 2: Reflect Point over the -axis
- Reflection over the -axis changes the sign of the -coordinate, so:
Final Answer:
The ordered pair that describes the location of is .
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:
- What are the coordinates of a point after a reflection over the origin?
- How do you reflect a point over the line ?
- What happens when you reflect a point twice over the same axis?
- How do you find the midpoint between two reflected points?
- What is the general formula for reflecting a point over a given line?
Tip: Remember, reflecting over the -axis only affects the -coordinate, while reflecting over the -axis only affects the -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