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. I hope this gives you more of an intuitive sense. If you want, you can connect each vertex and rotated vertex to the origin to see if the angle is indeed 90 degrees. As per the definition of rotation, the angles APA', BPB', and CPC', or the angle from a vertex to the point of rotation (where your finger is) to the transformed vertex, should be equal to 90 degrees. The rotated triangle will be called triangle A'B'C'. The point at which we do the rotation, we'll call point P. Well, let's say the shape is a triangle with vertices A, B, and C, and we want to rotate it 90 degrees. The shape is being rotated! But how do we do this for a specific angle? With your finger firmly on that point, rotate the paper on top. Now place your finger on the rotation point. Put another paper on top of it (I like to imagine this one as being something like a transparent sheet protector, and I draw on it using a dry-erase marker) and trace the point/shape. Here's something that helps me visualize it: The "formula" for a rotation depends on the direction of the rotation. I'm sorry about the confusion with my original message above. If you want to do a clockwise rotation follow these formulas: 90 = (b, -a) 180 = (-a, -b) 270 = (-b, a) 360 = (a, b). Also this is for a counterclockwise rotation. 360 degrees doesn't change since it is a full rotation or a full circle. 180 degrees and 360 degrees are also opposites of each other. So, (-b, a) is for 90 degrees and (b, -a) is for 270. The break even point is to sell 150 hot dogs.The way that I remember it is that 90 degrees and 270 degrees are basically the opposite of each other. Variable cost = fee charged for 1 hot dog × number of hot dogs sold R = selling price of 1 hot dog × number of hot dogs sold Let R be the revenue made for selling x hot dogs Let C be the cost of buying and selling x hot dogs However, the city hall charges him 1 dollar for each hot dog soldĬalculate the break even point if the price he charges for 1 hot dog is $1.50 The city allows him to sell his hot dogs somewhere near the city hall. It costs a man 75 dollars to buy the things that he needs to make hot dogs. The break even point is to sell 10000 books. Variable cost = fee charged for 1 book × number of books sold R = selling price of 1 book × number of books sold Let R be the revenue made for selling x books Let C be the cost of producing and selling x books If the company charges 9 dollars per book, how many books should they sell to break even? To help the publishing company sell the books, a marketing company charges 4 dollars for each book sold. The 50,000 is a fixed cost or a cost that cannot change. It costs a publishing company 50,000 dollars to make books.
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