Math Problem Statement

Where is U' after reflecting across the line y = 3?

Solution

To solve this problem, we need to reflect point UU across the line y=3y = 3.

Steps to Reflect Point UU Across y=3y = 3:

  1. Find the vertical distance from point UU to the line y=3y = 3.
  2. Reflect the point by moving it the same distance on the opposite side of the line.

Let's go step by step.

  1. Identify the coordinates of point UU from the image. Based on the grid, point UU appears to be at U(3,5)U(3, 5).
  2. The line y=3y = 3 is horizontal. To reflect U(3,5)U(3, 5) across this line:
    • Point UU's y-coordinate is 5.
    • The distance from y=5y = 5 to y=3y = 3 is 53=25 - 3 = 2.
    • Now reflect UU by subtracting the distance from 3: 32=13 - 2 = 1.

Therefore, the reflection of point U(3,5)U(3, 5) across y=3y = 3 is U(3,1)U'(3, 1).

Final Answer:

The coordinates of UU' are (3,1)(3, 1).

Would you like further details or have any questions?

Here are 5 relative questions to expand:

  1. How do you reflect points across a vertical line (like x=constantx = \text{constant})?
  2. What is the general formula for reflecting points across a horizontal line?
  3. How does reflecting across the origin differ from reflecting across a line?
  4. How would you describe the transformation properties of reflection in terms of distances and angles?
  5. Can reflections change the orientation of a figure?

Tip: When reflecting points across a horizontal or vertical line, only one coordinate (either xx or yy) 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