The line `2x-y = 5` turns about the point on it, whose ordinate and abscissae are equal through an angle of `45^@` in the anti-clockwise direction. Find the equation of the line in the new position.

The line 3x - 4y + 7 = 0 is rotated through an angle pi/4 in the clockwise direction about the point (-1, 1) . The equation of the line in its new position is

If the axes are rotated through an angle of 30^@ in the anti clockwise direction, then coordinates of point (4,-2sqrt3) with respect to new axes are

A line passing through the point A(3,0) makes 30^0 angle with the positive direction of x- axis . If this line is rotated through an angle of 15^0 in clockwise direction, find its equation in new position.

Two lines represented by the equation. x^2-y^2-2x+1=0 are rotated about the point (1,0) , the line making the bigger angle with the position direction ofthe x-axis being turned by 45^@ in the clockwise sense and the other line being turned by 15^@ in the anti-clockwise sense. The combined equation of the pair of lines in their new position is

A line through the point P (1, 2) makes an angle of 60^0 with the positive direction of x-axis and is rotated about P in the clockwise direction through an angle 15^0 . Find the equation of the straight line in the new position.

Let A be the image of (2, -1) with respect to Y - axis Without transforming the oringin, coordinate axis are turned at an angle 45^(@) in the clockwise direction. Then, the coordiates of A in the new system are

If the lines represented by x^(2)-2pxy-y^(2)=0 are rotated about the origin through an angle theta , one clockwise direction and other in anti-clockwise direction, then the equation of the bisectors of the angle between the lines in the new position is

The point (4,1) undergoes the following three successive transformations , reflection about the line y = x-1 translation through a distance 1 unit along the positive direction rotation thrpough an angle pi/4 about the origin in the anti - clockwise direction Then the coordinates of the final point are ,

If the axes are rotated through an angle of 45^(@) in the clockwise direction, the coordinates of a point in the new systeme are (0,-2) then its original coordinates are

The point (4, 1) undergoes the following three transformations successively: (a) Reflection about the line y = x (b) Translation through a distance 2 units along the positive direction of the x-axis. (c) Rotation through an angle pi/4 about the origin in the anti clockwise direction. The final position of the point is given by the co-ordinates.