Math Problem Statement
Where is U' after reflecting across the line y = 3?
Solution
To solve this problem, we need to reflect point across the line .
Steps to Reflect Point Across :
- Find the vertical distance from point to the line .
- Reflect the point by moving it the same distance on the opposite side of the line.
Let's go step by step.
- Identify the coordinates of point from the image. Based on the grid, point appears to be at .
- The line is horizontal. To reflect across this line:
- Point 's y-coordinate is 5.
- The distance from to is .
- Now reflect by subtracting the distance from 3: .
Therefore, the reflection of point across is .
Final Answer:
The coordinates of are .
Would you like further details or have any questions?
Here are 5 relative questions to expand:
- How do you reflect points across a vertical line (like )?
- What is the general formula for reflecting points across a horizontal line?
- How does reflecting across the origin differ from reflecting across a line?
- How would you describe the transformation properties of reflection in terms of distances and angles?
- Can reflections change the orientation of a figure?
Tip: When reflecting points across a horizontal or vertical line, only one coordinate (either or ) changes, while the other remains the same.
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Math Problem Analysis
Mathematical Concepts
Geometry
Reflections
Coordinate Plane
Formulas
Reflection Formula: For a point (x, y) reflected across y = c, the new y' coordinate is y' = 2c - y.
Theorems
Reflection Theorem: A reflection across a horizontal line changes only the y-coordinate, keeping the x-coordinate constant.
Suitable Grade Level
Grades 6-8