1.

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 coordinates are with respect to old axis are:°

Answer»

The new coordinates (X,Y) are given as:

x=X Cos a - Y Sin a

y= Xsin a + Y Cos a;

Where a = angle of rotation, X and Y are given coordinates

As the axis is roted by 30° in negative direction then angle of rotation is written as (-30°)

So, x = 2 cos(-30°) -  1 sin (-30°)
= 2√3/2 + 1/2
= √3 + 1/2 = (2√3 +1)/2

again y = 2 sin (-30°) + 1 cos(-30°)
= -2/2 + √3/2  = -1 + √3/2  = (-2 + √3)/2


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