Question
Use the diagram below to find the coordinates of AKJV after a rotation of 90° counterclockwise about the point
(-1, 1)
(-1, 1)
Answers
Answered by
GPT 3.5
To find the coordinates of a point after a rotation of 90° counterclockwise about a given point, we can use the following formula for rotation:
(x', y') = (x - h, y - k)
(cosθ, sinθ)
+ (h, k)
Where (x, y) are the original coordinates of the point, (x', y') are the coordinates after rotation, (h, k) are the coordinates of the center of rotation, and θ is the angle of rotation.
In this case, the center of rotation is (-1, 1) and the angle of rotation is 90°.
For point A with coordinates (-2, 3), we have:
(x', y') = (-2 - (-1), 3 - 1)
(cos90°, sin90°)
+ (-1, 1)
= (-2 + 1, 3 - 1)
(0, 1)
+ (-1, 1)
= (-1, 2)
(0, 1)
+ (-1, 1)
= (-1, 3)
Therefore, after a rotation of 90° counterclockwise about the point (-1, 1), the coordinates of AKJV become (-1, 3).
(x', y') = (x - h, y - k)
(cosθ, sinθ)
+ (h, k)
Where (x, y) are the original coordinates of the point, (x', y') are the coordinates after rotation, (h, k) are the coordinates of the center of rotation, and θ is the angle of rotation.
In this case, the center of rotation is (-1, 1) and the angle of rotation is 90°.
For point A with coordinates (-2, 3), we have:
(x', y') = (-2 - (-1), 3 - 1)
(cos90°, sin90°)
+ (-1, 1)
= (-2 + 1, 3 - 1)
(0, 1)
+ (-1, 1)
= (-1, 2)
(0, 1)
+ (-1, 1)
= (-1, 3)
Therefore, after a rotation of 90° counterclockwise about the point (-1, 1), the coordinates of AKJV become (-1, 3).