This video is part of Khan Academys geometry course, which offers free, world-class education for anyone, anywhere. You will see examples of how to find the coordinates of the reflected points and how to check your answers. So from 0 degrees you take (x, y) and make them negative (-x, -y) and then you've made a 180 degree rotation. Watch this video to learn how to reflect points in the coordinate plane using the x-axis, y-axis, or any other line. 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. Using the formulas of coordinate geometry how can we help Ron to find the other end of the diameter of the circle Solution: Let (AB) be the diameter of the circle with the coordinates of points (A ), and (B) as follows. Next, create a second line segment of the same length, 3 units, with one endpoint at the origin. Note that the length of this segment is 3 units. You will learn how to perform the transformations, and how to map one figure into another using these transformations. Then, create a line segment connecting A to the origin. 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. If you understand everything so far, then rotating by -90 degrees should be no issue for you. Example 1: Ron is given the coordinates of one end of the diameter of a circle as (5, 6) and the center of the circle as (-2, 1). First, plot the point on the coordinate plane. 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. Our point is at (-1, 2) so when we rotate it 90 degrees, it will be at (-2, -1) 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. A rotation is a type of transformation that turns a figure around a fixed point. When you rotate by 90 degrees, you take your original X and Y, swap them, and make Y negative. If you have a point on (2, 1) and rotate it by 90 degrees, it will end up at (-1, 2) In case the algebraic method can help you:
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