Rotations
Rotations, a fundamental concept in mathematics and physics, play a pivotal role in transforming objects, vectors, or coordinate systems around a fixed point or axis. Essential in various fields including geometry, computer graphics, robotics, and engineering, rotations provide a framework to understand spatial transformations. Whether it's a simple rotation of a 2D shape or complex rotations in 3D space, mastering this concept enables precise manipulation and analysis of spatial data. This introduction delves into the significance and applications of rotations, elucidating their importance in modeling real-world phenomena and facilitating problem-solving across diverse disciplines.
Questions
- Point A is at #(1 ,3 )# and point B is at #(2 ,-1 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(-7 ,-1 )# and point B is at #(2 ,-4 )#. Point A is rotated #pi # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(2 ,9 )# and point B is at #(-8 ,-3 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(-3 ,4 )# and point B is at #(-8 ,1 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- A line segment with endpoints at #(5 , -9 )# and #(2, -7 )# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?
- Point A is at #(-8 ,2 )# and point B is at #(7 ,-1 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- A line segment with endpoints at #(5 , -2 )# and #(2, -7 )# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?
- Point A is at #(4 ,-5 )# and point B is at #(-6 ,-2 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- The coordinates of a polygon are (2, 3), (4,7), (8,5), and (7,2). If the polygon rotates 90° clockwise about the origin, in which quadrant will the transformation lie? What are the new coordinates?
- Point A is at #(9 ,3 )# and point B is at #(1 ,-3 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(5 ,2 )# and point B is at #(2 ,-4 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(-8 ,5 )# and point B is at #(-3 ,-2 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(-1 ,-5 )# and point B is at #(-2 ,4 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(-2 ,5 )# and point B is at #(-3 ,3 )#. Point A is rotated #pi # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(6 ,7 )# and point B is at #(-3 ,4 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- A line segment with endpoints at #(3 , -2 )# and #(5, 8 )# is rotated clockwise by #(3 pi)/2#. What are the new endpoints of the line segment?
- Point A is at #(5 ,-2 )# and point B is at #(-2 ,5 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Point A is at #(-2 ,-8 )# and point B is at #(-5 ,3 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- A line segment with endpoints at #(5, 1)# and #(7, 2)# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?
- Point A is at #(9 ,-2 )# and point B is at #(2 ,4 )#. Point A is rotated #pi # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?