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Question

The line joining two points A(2,0),B(2+3,1) is rotated about A in anti-clockwise direction through an angle of 30. If the coordinates of new position of B is (h,k), then the value of h2+k2 is

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Solution

Distance AB=(3)2+12=2 units
The slope of the line AB is given by
m=102+32=13
tanθ=13θ=π6
The line makes on angle of 30 with xaxis.
AB is rotated through 30about point A in anticlock wise. So, it makes an angle of 60 with xaxis.
The new coordinates of B is
(2+ABcosθ,0+ABsinθ)=(2+2cos60,2sin60)=(3,3)h2+k2=9+3=12

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