And now we can do thatįor each of the points. This right triangle 90 degrees, your new point I, maybe I shouldn't say, I'll call it I prime, which is what is the image of this point after I've done the 90 degree rotation is going to be right over here. So your new point I, if you rotate this triangle, So that green line, let meĭraw the hypotenuse now, it's gonna look like, oops, I wanted to do that in a different color. The corresponding point in the image after the rotation is going to be right over here. So you're gonna go to the right seven, just like this. Instead of going down seven, you're going to go to the right seven. You're gonna go straight as a right angle and Side and this blue side, so you're gonna form a right angle again. But if you were to rotate it up, notice this forms a right angle between this magenta
What about, what about this side right over here? Well this side over here, notice we've gone down from the origin, we've gone down seven. Now what about this side over here? What about this side? Let me do this in a different color. So that's rotating it 90 degrees, just like that. Rotate it positive 90 degrees, that side it going to look like this. Seven along the x-axis, it's going to go seven along the y-axis. So what's going to happen there? Well this side, right over here, if I rotate this 90 degrees, where is that going to go? Well instead of going Now if I'm gonna rotate I 90 degrees about the origin, that'sĮquivalent to rotating this right triangle 90 degrees. So let me see if I can, It's I could probably draw, actually I can use a line tool for that. So, it's a right triangle where the line between the origin and I is its hypotenuse. So let's first focus on, actually let's first focus
But how do we do that? And to do that, what I am going to do, to do that what I'm gonna do is I'm gonna draw a series Those around the origin by positive 90 degrees. Just focus on the vertices, because those are theĮasiest ones to think about, to visualize. Rotate the points here around the origin by negative 270 degrees, that's equivalent to just rotating all of the points, and I'll That this is equivalent to a positive 90 degree rotation. Get that point here, which we could have also gotten there by just rotating it by And then this would beĪnother negative 90, which would give you in total, negative 270 degrees.
This would be rotatingĪnother negative 90, which would, together, be negative 180. The origin by negative, so this is the origin here, by negative 270 degrees, what would that be? Well let's see, this wouldīe rotating negative 90. If you were to start right over here and you were to rotate around
So if I were to start, if I were to, let me draw some coordinate axes here. So let's just first thinkĪbout what a negative 270 degree rotation actually is. So actually let me go over here so I can actually draw on it. The points of this triangle around the origin by negative 270 degrees, where is it gonna put these points? And to help us think about that, I have copied and pasted So what we want to do is think about, well look, if we rotate And this tool, I can put points in, or I could delete points. So positive is counter-clockwise, which is a standard convention, and this is negative, so a negative degree would be clockwise. The direction of rotationīy a positive angle is counter-clockwise. So this is the triangle PINĪnd we're gonna rotate it negative 270 degrees about the origin. We're told that triangle PIN is rotated negative 270ĭegrees about the origin.