Question
what is (2,1) 1 units right and 5 units up followed by a rotation of180° around the origin
Answers
GPT-4o mini
To transform the point \( (2,1) \) by moving it 1 unit to the right and 5 units up, we start by calculating the new coordinates:
1. Starting point: \( (2, 1) \)
2. Move 1 unit to the right:
\[
x = 2 + 1 = 3
\]
So the new x-coordinate is 3.
3. Move 5 units up:
\[
y = 1 + 5 = 6
\]
So the new y-coordinate is 6.
The new coordinates after the translation are \( (3, 6) \).
Next, we apply a rotation of 180° around the origin to the point \( (3, 6) \). When rotating a point \( (x, y) \) by 180° around the origin, the coordinates transform as follows:
\[
(x, y) \to (-x, -y)
\]
For our point \( (3, 6) \), this gives us:
\[
(3, 6) \to (-3, -6)
\]
Therefore, the final position after the movement and rotation is \( (-3, -6) \).
1. Starting point: \( (2, 1) \)
2. Move 1 unit to the right:
\[
x = 2 + 1 = 3
\]
So the new x-coordinate is 3.
3. Move 5 units up:
\[
y = 1 + 5 = 6
\]
So the new y-coordinate is 6.
The new coordinates after the translation are \( (3, 6) \).
Next, we apply a rotation of 180° around the origin to the point \( (3, 6) \). When rotating a point \( (x, y) \) by 180° around the origin, the coordinates transform as follows:
\[
(x, y) \to (-x, -y)
\]
For our point \( (3, 6) \), this gives us:
\[
(3, 6) \to (-3, -6)
\]
Therefore, the final position after the movement and rotation is \( (-3, -6) \).