Rotating a PointDate: 04/08/2003 at 09:19:04 From: Reggie Subject: Coordinates on a grid What is the formula for figuring out the coordinates to answer a question like: Find the image of a triangle with vertices A(0,1),B(-2,0) and C(-4,-5) under a rotation of 90 degrees counterclockwise about the origin. Is there a formula I can use instead of drawing a picture? Date: 04/08/2003 at 12:42:55 From: Doctor Rick Subject: Re: Coordinates on a grid Hi, Reggie. Yes, there is, but I suggest that you graph one point anyway. You can discover the formula by examining how the coordinates of that one point change under this rotation. Then you can apply the same formula to the other points. Take any one of the points - I suggest C, because it's not on either axis - and find the coordinates of the rotated point. Hint: You can rotate the point by turning the whole page counterclockwise 90 degrees. y x ^ ^ | | | | | | -4 | | -5 -----+-----+--------->x ===> y<-----------+-------+---- : | | : : | | : : | -4+.......* *.....+-5 | | | Then relabel the axes the right way. You want to rotate the point but NOT the axes. y ^ | | | | 5 ------------+-------+---->x | : | : -4+.......* | | What was the positive x-axis is now pointing up, so it is where the positive y-axis should be. Therefore, what was the x-coordinate is now the y-coordinate. On the other hand, what was the positive y-axis is now the NEGATIVE x-axis. It is pointing left. How is the new x-coordinate related to the old y-coordinate? These observations will help you to write down not only the coordinates of the rotated point, but a rule for changing the old coordinates to the new coordinates. This rule could be applied to any point. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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