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. (Click Here for Help Video)(1 point) Point B's final position is: Skip to navigation page 12 of 13 point b is 2,1
Answers
GPT-4o mini
To find the final position of point B (which is initially at coordinates (2, 1)) after the given transformations, we will follow the sequential steps of the translation and rotation.
1. **Translation of 5 units to the right:**
- To translate a point to the right, we add to its x-coordinate.
- Original point B: (2, 1)
- After translating 5 units to the right:
\[
(2 + 5, 1) = (7, 1)
\]
2. **Translation of 4 units up:**
- To translate a point upward, we add to its y-coordinate.
- Current position after the first translation: (7, 1)
- After translating 4 units up:
\[
(7, 1 + 4) = (7, 5)
\]
3. **Rotation of 180° around the origin:**
- To rotate a point 180° around the origin, we negate both the x and y coordinates (change their signs).
- Current position before rotation: (7, 5)
- After rotating 180°:
\[
(-7, -5)
\]
Therefore, the final position of point B after all transformations is **(-7, -5)**.
1. **Translation of 5 units to the right:**
- To translate a point to the right, we add to its x-coordinate.
- Original point B: (2, 1)
- After translating 5 units to the right:
\[
(2 + 5, 1) = (7, 1)
\]
2. **Translation of 4 units up:**
- To translate a point upward, we add to its y-coordinate.
- Current position after the first translation: (7, 1)
- After translating 4 units up:
\[
(7, 1 + 4) = (7, 5)
\]
3. **Rotation of 180° around the origin:**
- To rotate a point 180° around the origin, we negate both the x and y coordinates (change their signs).
- Current position before rotation: (7, 5)
- After rotating 180°:
\[
(-7, -5)
\]
Therefore, the final position of point B after all transformations is **(-7, -5)**.