Question
Figure reflected over the x axis which statement describe the effect of the reflection on the x and y coordinates of each vertex
X coordinate of each vertex stay the same
Y coordinate of each vertex stay the same
X coordinate of each vertex changes to opposite
Y coordinate of each vertex changes to opposite
X coordinate of each vertex stay the same
Y coordinate of each vertex stay the same
X coordinate of each vertex changes to opposite
Y coordinate of each vertex changes to opposite
Answers
GPT-4o mini
When a figure is reflected over the x-axis, the following effects occur on the coordinates of each vertex:
- The **x-coordinate of each vertex stays the same**: This is true because a reflection over the x-axis does not change the horizontal position of the points.
- The **y-coordinate of each vertex changes to the opposite**: This is also true because reflecting over the x-axis inverts the vertical position of each point. If the original y-coordinate is \(y\), the reflected y-coordinate becomes \(-y\).
So, the correct statements are:
1. X coordinate of each vertex stays the same.
2. Y coordinate of each vertex changes to opposite.
- The **x-coordinate of each vertex stays the same**: This is true because a reflection over the x-axis does not change the horizontal position of the points.
- The **y-coordinate of each vertex changes to the opposite**: This is also true because reflecting over the x-axis inverts the vertical position of each point. If the original y-coordinate is \(y\), the reflected y-coordinate becomes \(-y\).
So, the correct statements are:
1. X coordinate of each vertex stays the same.
2. Y coordinate of each vertex changes to opposite.