![]() So from 0 degrees you take (x, y) and make them negative (-x, -y) and then you've made a 180 degree rotation. A rotation is an isometric transformation that turns every point of a figure through a specified angle and direction about a fixed point. When you rotate by 180 degrees, you take your original x and y, and make them negative. ![]() If you have a point on (2, 1) and rotate it by 180 degrees, it will end up at (-2, -1) We do the same thing, except X becomes a negative instead of Y. If you understand everything so far, then rotating by -90 degrees should be no issue for you. Our point is as (-2, -1) so when we rotate it 90 degrees, it will be at (1, -2)Īnother 90 degrees will bring us back where we started. ![]() What about 90 degrees again? Same thing! But remember that a negative and a negative gives a positive so when we swap X and Y, and make Y negative, Y actually becomes positive. A positive degree rotation runs counter clockwise and a negative degree rotation runs clockwise. The general rule for a rotation by 180 about the origin is (A,B) (-A, -B) Rotation by 270 about the origin: R (origin, 270) A rotation by 270 about the origin can be seen in the picture below in which A is rotated to its image A'. Create your own worksheets like this one with Infinite Geometry. What are Rotations Rotations are a type of transformation in geometry where we take a point, line, or shape and rotate it clockwise or counterclockwise, usually by 90,180, 270, -90, -180, or -270. Our point is at (-1, 2) so when we rotate it 90 degrees, it will be at (-2, -1) rotation 90 counterclockwise about the origin. What if we rotate another 90 degrees? Same thing. So from 0 degrees you take (x, y), swap them, and make y negative (-y, x) and then you have made a 90 degree rotation. You will learn how to perform the transformations, and how to map one figure into another using these transformations. When you rotate by 90 degrees, you take your original X and Y, swap them, and make Y negative. In this topic you will learn about the most useful math concept for creating video game graphics: geometric transformations, specifically translations, rotations, reflections, and dilations. Its just that when I tried to prove the statement that the second point will take on the coordinate of (-y,x), I ended up with 2 results since I didnt incorporate the direction of rotation into my calculation. If you have a point on (2, 1) and rotate it by 90 degrees, it will end up at (-1, 2) begingroup DreiCleaner Hi, thanks for helping Yes, the second point is the resultant point after the rotation. In case the algebraic method can help you:
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |