Question

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?

Answer 1

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).