Question

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.
A. `(2+(1)/(sqrt(2)),sqrt(3))`
B. `(2+(1)/(sqrt(2)),(sqrt(3))/(2))`
C. `(2+(1)/(sqrt(2)),(sqrt(3))/(2))`
D. `(2-(1)/(sqrt(2)),-(sqrt(3))/(2))`

Answer 1

Correct Answer - D
The equation of AC is
`(x-2)/(cos 60^(@))=(y-0)/(sin 60^(@))=r`
We have , AB `=sqrt((3-2)^(2)+(1-0)^(2))=sqrt(2)`
As AC is the new position of AB. Therefore, AC =`AB=sqrt(2)` .
Thus, the coordinates of C are given by
`(x-2)/(cos 60^(@))=(y-0)/(sin 60^(@))=sqrt(2) implies x=2+(1)/(sqrt(2)),y=sqrt((3)/(2))`
Hence , the coordinate of C are `(2+(1)/(sqrt(2)),sqrt((3)/(2)))`.