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Question

A line segment AB of length 2 units, where A=(1,0) is rotated in anticlockwise direction through an angle 15 about A. If initially AB is making an angle 45 with the positive direction of X- axis in anticlockwise direction, then the distance between origin and the new position of B is

A
5
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B
7
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C
23
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D
1
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Solution

The correct option is B 7
Let B is the new position of B,

Given that AB makes an angle 60 with the positive direction of X-axis.

A=(1,0), AB=r=2, θ=60
Now,
B=(x1+rcosθ,y1+rsinθ)B=(1+2×cos60,0+2×sin60)
B=(1+2×12,0+2×32)B=(2,3)

So, the distance of B from origin
=(2)2+(3)2=7

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