If tha point P( 4,3) is rotated through an angle of 45⁰ in anti-clockwise direction about the origin, then coordinates of P in new position are ? Explain how ?

Dear Aditi,

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

x=X Cosa - Y Sina

y= XCosa +Y Sina;

a = angle of rotation,

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But here the point is rotated and not the axis....so can we use the same formula as applicable to the rotation of axis???

z= 4+3i

Let the new co-ordinate after rotation be z₁ .

z₁ = z*e^(i.pi/4) = (4+3i)*(cos(pi/4) + i.sin(pi/4)) = 1/sqrt(2)* (4+3i)(1+i) = 1/sqrt(2)* (1+7i)

New Point = ( 1/sqrt(2), 7/sqrt(2) )

it will remain (4,3)..lolz