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Question

A line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction through an angle 15. If B goes to C in the new position, then the coordinates of C are


A

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B

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C

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D

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Solution

The correct option is C


Slope of line

AB=0123=1=tan 45 BAX=45

Given CAB=15 CAX=60 Slope of the AC=tan 60=3

Now, line AC makes an angle of 60 with positive direction of x-axis and

AC=AB=(32)2+(10)2=2

Coordinates of C are 2+2 cos 60,0+2sin 60

i.e. (2+12,32)


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