Question
Trapezoid `KLMN`is reflected over the x-axis to form trapezoid `WXYZ`. Which statement is true?
Answers
Answered by
GPT-4o mini
When trapezoid \( KLMN \) is reflected over the x-axis to form trapezoid \( WXYZ \), the following transformations occur for each point in the trapezoid:
- Points that lie above the x-axis will have their y-coordinates negated (inverted) while keeping their x-coordinates the same.
- Points that lie below the x-axis will have their y-coordinates negated as well.
- Points that lie exactly on the x-axis will remain unchanged.
Thus, if you have a point \( (x, y) \) in trapezoid \( KLMN \), after reflection over the x-axis, the corresponding point in trapezoid \( WXYZ \) will be \( (x, -y) \).
From this, you can conclude the following:
- The x-coordinates of corresponding points in trapezoid \( WXYZ \) will be the same as those in trapezoid \( KLMN \).
- The y-coordinates will be the negatives of the y-coordinates of trapezoid \( KLMN \).
Based on this transformation, a true statement about the trapezoids relates to their coordinates after the reflection. If you would like, I can help you understand what specific statements might be true based on the coordinates of trapezoid \( KLMN \).
- Points that lie above the x-axis will have their y-coordinates negated (inverted) while keeping their x-coordinates the same.
- Points that lie below the x-axis will have their y-coordinates negated as well.
- Points that lie exactly on the x-axis will remain unchanged.
Thus, if you have a point \( (x, y) \) in trapezoid \( KLMN \), after reflection over the x-axis, the corresponding point in trapezoid \( WXYZ \) will be \( (x, -y) \).
From this, you can conclude the following:
- The x-coordinates of corresponding points in trapezoid \( WXYZ \) will be the same as those in trapezoid \( KLMN \).
- The y-coordinates will be the negatives of the y-coordinates of trapezoid \( KLMN \).
Based on this transformation, a true statement about the trapezoids relates to their coordinates after the reflection. If you would like, I can help you understand what specific statements might be true based on the coordinates of trapezoid \( KLMN \).