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

Step-by-step solution

The coordinates of point A are (2, 0) and B are (3, 1) . The vector AB is given by (3-2, 1-0) = (1, 1) . The length of AB is r = 1^2 + 1^2 = 2 . The angle that AB makes with the positive x-axis is ⁻¹( 1 1 ) = 45^ . When the line is rotated anticlockwise about A by 15^ , the new angle of the line AC with the positive x-axis becomes 45^ + 15^ = 60^ . The coordinates of C are given by (x_A + r (60^ ), y_A + r (60^ )) . Substituting the values, x_C = 2 + 2 (60^ ) = 2 + 2 1 2 = 2 + 1 2 . y_C = 0 + 2 (60^ ) = 2 3 2 = 3 2