What transformations should a student apply to map triangle ABC onto triangle A''B''C'' after performing a reflection over the x-axis?
To map triangle ABC onto triangle A''B''C'' after performing a reflection over the x-axis, the following transformations should be applied:
1. Reflection over the x-axis: This transformation can be achieved by changing the sign of the y-coordinates of each point. For example, if point A has coordinates (x1, y1), after reflecting over the x-axis, it will have coordinates (x1, -y1).
2. No other transformations: In this case, after the reflection over the x-axis, the triangle will already be mapped onto triangle A''B''C''. No additional transformations are required.
Therefore, the only transformation needed is the reflection over the x-axis.
To map triangle ABC onto triangle A''B''C'' after performing a reflection over the x-axis, a student should apply the following transformations:
1. Reflect the vertices of triangle ABC over the x-axis to get triangle A'B'C'.
- To perform this reflection, the student needs to take each vertex of triangle ABC and change its y-coordinate to its opposite value.
2. Once triangle A'B'C' is obtained, the student should then translate it to the new position of triangle A''B''C''.
- The translation can be done by shifting each vertex of triangle A'B'C' according to the difference in x and y coordinates between the corresponding vertices of triangle A''B''C'' and A'B'C''.
By applying the reflection and translation, triangle ABC can be mapped onto triangle A''B''C'' after the reflection over the x-axis.