![]() ![]() *Why does the x become negative?* That's because the point going down into the negative quadrant. The point (-3,6), is among one of those points. *Why do the coordinates flip?* Imagine there's a circle in the grid, telling you all the points of where (6,3) can be rotated to. Following the pattern of the equation, it becomes (-3,6). I'm going to rotate that point -90 (clockwise) around the origin. Let's start by using coordinates (6,3) as an example. It's definitely a bit puzzling, so here's what I gathered: Remember! A negative and a negative gives a positive! So if we rotate another 180 degrees we go from (-2, -1) to (2, 1)Īnd if we have another point like (-3, 2) and rotate it 180 degrees, it will end up on (3, -2) So from 0 degrees you take (x, y) and make them negative (-x, -y) and then you've made a 180 degree rotation. 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. 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. 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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