Question

Where is point B after a translation of 5 unit right, then 4 units up, followed by a rotation of 180°
around the origin.
B=(2,1)
Point B's final position is:

Answer 1

To find the final position of point B after the specified transformations, we follow these steps:

1. **Original point B**: \( B = (2, 1) \)

2. **Translation of 5 units right**:
- This means we add 5 to the x-coordinate:
\[
(2 + 5, 1) = (7, 1)
\]

3. **Translation of 4 units up**:
- This means we add 4 to the y-coordinate:
\[
(7, 1 + 4) = (7, 5)
\]

4. **Rotation of 180° around the origin**:
- To rotate a point \( (x, y) \) by 180° around the origin, the new coordinates will be \( (-x, -y) \):
\[
(7, 5) \rightarrow (-7, -5)
\]

Therefore, after the translations and the rotation, point B's final position is:
\[
\boxed{(-7, -5)}
\]