The line joining the points A (1, 1) and B (4, 4) is rotated about A in the anti-clockwisedirection through an angle of 15Â°, find the equation of the line in the new position. If B goes to C. findthe coordinates of C.

The line joining the points A (1, 1) and B (4, 4) is rotated about A i

1.	The line joining the points A (1, 1) and B (4, 4) is rotated about A in the anti-clockwisedirection through an angle of 15Â°, find the equation of the line in the new position. If B goes to C. findthe coordinates of C.
Answer» Slope of line AB4-1/4-13/3tan theta= 145°let after rotation the point B reaches to the point C.such that∠CAB=15thus the slope of the line CA betan(45+15)=tan60=√3the coordinates of the point A are (1,1))therefore the equation of the line CA isy-y₁= m(x-x₁)y-1= √3(x-1)