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Keeping the origin constant axes are rotated at an angle 30° in negative direction, if then new coordinates of the point are (2,1) then its coordinate are with respect to old axis are |
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Answer» Let the line segment joining the origin and the new position of the point (2,1) with respect to new axes subtends angle A with the new X-axis and let the length of the segment be r. So rcosA=2 and rsinA=1 With respect to the old position of the axes the line segment will subtend an angle (A-30)° with the X-axis. So x-cordinate of the point w r to old axes will be x=rcos(A-30) =rcosAcos30°+rsinAsin30° =2×(√3/2)+1×1/2 =(2√3+1)/2 And corresponding y-coordinate. y=rsin(A-30) =rsinAcos30°-rcosAsin30° =1×√3/2-2×1/2 =(√3-2)/2 Hence option (B) accepted |
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