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Question

A line joining two points A(2,0) and B(3,1) is rotated about A in anti-clockwise direction through an angle 150. If goes to C in the new position, then the coordinates of C are

A
(2,32)
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B
(2,32)
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C
(2+12,32)
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D
None of these
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Solution

The correct option is C (2+12,32)
(c) Slope of line AB=0123=1=tan450
BAX=450
Given CAB=150
CAX=600
Slope of line AC=tan600=3
Now line AC makes an angle of 600 with positive direction ofx-axis and
AC=AB=(32)2+(10)2=2
Co-ordinates of C are (2+2cos600,0+2sin600)
i.e.,(2+12,32)

459204_38363_ans_5311dc9a2013486faff89033edbb81e9.png

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