Finding the coordinates of a point rotated about the origin

Question: Rotating a point around another using vectors. - method is wrong?
The question: On what coordinates will point B = (7,5) land if it is rotated around point A = (0,0) by 110 degrees?My workings out gave me the answer B will land on point (-7.09, 4.87). I got this answer by figuring out that the vector from A to B is (7 , 5) and therefore the direction angle of the vector AB is tan^-1(5/7) = 35.54° by using pythagoras on vector AB. Thus the direction angle of AB1, where B1 is the new point on which B will land, is 110 + 35.54 = 145.54 degrees. Then, one can use the rule that the unit vector in the unit circle is (cos(v), sin(v)), and by finding out the length of the vector AB (√(7^2+5^2 = √74)), you can apply this rule to the new AB1 vector and you get that the vector AB1 = √74 * (cos(145.54°) , sin(145.54°)). This, in turn, is equal to AB1 = (-7.09, 4.87). Now that we have the vector of AB1, we can use this to find point B1, by adding the values inside vector AB1 to the point we are rotating B around (A = (0,0)). Therefore B1 = (-7.0...

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Answered By:

Richard C.
Confidence-building Geometry tutor with 18 years experience

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