The line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of `15^@`. find the equation of line in the new position. If b goes to c in the new position what will be the coordinates of C.

Explanation

Given,AB is rotated through an angle `15^0` in anticlockwise direction about `A` and point `B` goes to `C`

So, inclination of line `AC` is `60^0`.

The coordinate of `A` is `(2,0)` and `c` is `(x_1,y_1)`
So,equation of line `AC` is

`(x-x_1)/(costheta)=(y-y_1)/(sintheta)=r`


`(x−2)/(cos60^0)-(y)/(sin60^0)=r`

`=>(x−2)/(1/2)=(y)/((sqrt3)/2)=r->(1)`


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