The point `(4,3)` when the axes translated to the point `(3,1)` and then axes are rotated through `30^@` about the origin, then the new position of the point is

The point (4,3) is translated to the point (3,1) and then the axes are rotated through an angle of 30^(@) about the origin,then the new coordinates of the point ((1)/(sqrt(2)),(sqrt(3)-1)/(2)) , ((sqrt(3)+2)/(2),(2sqrt(3)+1)/(2)) , ((sqrt(3))/(2),(2sqrt(3))/(5)) , ((sqrt(3)+2)/(2),(2sqrt(3)-1)/(2))

If the origin is shifted to the point O(2,3) the axes remaining parallel to the original axes the new co-ordinate of the point A (1,3) is ….

If the origin is shifted to (1,-2) and axis are rotated through an angle of 30^(@) the co- ordinate of (1,1) in the new position are

A point (1,1) undergoes reflection in the x-axis and then the cordinates axes are rotated through an angle of (pi)/(4) in anticlockwise direction.The final position of the point in the new coordinate system is

A point (2,2) undergoes reflection in the x . axis and then the coordinate axe are rotated through an angle of (pi)/(4) in anticlockwise direction.The final position of the point in the new coordinate system is

The point represented by the complex number 2+i rotated about the origin through an angle (pi)/(2) . The new position of the point is

The point (7,5) undergoes the following transformations successively (i) The origin is translated to (1,2). (ii) Translated through 2 units along the negative direction of the new X-axis alii) Rotated through an angle about the origin in the clockwise direction.The final position of the point (7,5) is

The point represented by the complex number 2-i is rotated about origin through on angle pi/2 the clockwise direction, the new position of the point is

If the axes are translated to the point (-2,-3) then the equation x^2+3y^2+4x+18y+30=0 transforms to