Where is point B after a translation of 5 units right, then 4 units up, followed by the rotation of 180 degrees around the origin.
Point B’s final position is?
To find the final position of point B, we need to perform the translation and rotation steps.
1. Start with the original position of point B.
2. Translate 5 units to the right. This means adding 5 to the x-coordinate of point B.
3. After the translation, we have a new point B' with coordinates (x + 5, y).
4. Translate 4 units up. This means adding 4 to the y-coordinate of point B'.
5. After the second translation, we have a new point B'' with coordinates (x + 5, y + 4).
6. Rotate 180 degrees around the origin. This means negating both the x and y coordinates of point B''.
7. After the rotation, the final position of point B is (-x - 5, -y - 4).
Therefore, the final position of point B is (-x - 5, -y - 4).