Which choice shows the image of triangle QRS after the reflection over the x-axis followed by a rotation of 180° around the origin?
1. Original
2. New QRS
3. New RQS
4. New SQR
Which choice shows the image of triangle QRS after the reflection over the x-axis followed by a rotation of 180° around the origin?
Share
To determine the resulting image of triangle QRS after a reflection over the x-axis followed by a 180° rotation around the origin, follow these steps:
1. Reflection Over the x-axis: This reflection changes the y-coordinates of each vertex of triangle QRS to their negative values. For example, if the original points of QRS are (x, y), after the reflection over the x-axis, the new coordinates would be (x, -y).
2. Rotation of 180° Around the Origin: This rotation alters the coordinates again, changing (x, -y) to (-x, -(-y)), which becomes (-x, y). In essence, this negates both the x and y coordinates.
Now, if you apply both transformations to the vertices of triangle QRS, you’ll arrive at the final coordinates. The correct choice will be the one that matches these final coordinates after both transformations.
To find the exact answer out of the provided options (1-4), you’ll need to compare the transformed coordinates with the images shown.
Remember to check the specific images linked to your question for confirmation! If you need further assistance, feel free to explore the extended services page.