Math Problem Statement
Solution
The task involves reflecting the triangle to its image over the x-axis. You need to determine the coordinates of the reflected image points , which correspond to points after reflection.
Coordinates of :
Reflection rule:
When reflecting over the x-axis, the y-coordinate of each point changes sign, while the x-coordinate remains the same. The reflection formula is:
Applying the reflection:
- For point , the reflection is .
- For point , the reflection is .
- For point , the reflection is .
Completed table:
Explanation in words:
To map to , you reflect each vertex over the x-axis. This means for every point, the x-coordinate stays the same, while the y-coordinate changes sign. For example, point is reflected to , and the same rule applies to the other points.
Would you like more details or have any questions?
Additional questions:
- What happens if you reflect over the y-axis instead of the x-axis?
- How would the coordinates change if you reflected the triangle over both the x- and y-axes?
- What is the distance between point and its reflection ?
- How can you use the reflection formula to determine if two points are symmetric with respect to the x-axis?
- Can you describe the transformation if the triangle is reflected over a diagonal line like ?
Tip:
Reflections maintain the size and shape of a figure, but they reverse the orientation relative to the axis of reflection.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Geometry
Reflections
Coordinate Plane
Formulas
Reflection across the x-axis: (x, y) → (x, -y)
Theorems
Reflection Theorem
Suitable Grade Level
Grades 8-10