Write the new coordinates of the following point (0,5) when the axes are rotated through to an angle `30^0`

If the coordinates of a point P are transformed to (4,-3) when the axes are rotated through an angle of 135^(0) , then find P.

If the coordiantes of a point P are transformed to (2,-4sqrt(3)) when the axes are rotated through an angle 60^(@) , then P=

Write the coordinates the reflections of point (3,\ 5) in X and Y -axes.

Write the coordinates of the points marked on the axes in Fig. 3.12.

Find the transformed equation of x^(2)+2sqrt3 xy-y^(2) = 2a^(2) when the axes are rotated through an angle 30^(0).

Find the transformed equation of 3x^(2)+10xy +3y^(2) = 9 when the axes are rotated through an angle pi/4

The transformed equation of x cos alpha + y sin alpha = p when the axes are rotated through an angle alpha is

The transformed equation of x^(2)+6xy+8y^(2)=10 when the axes are rotated through an angled pi//4 is

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

What are the coordinates of the image of the point (1, 0) on the terminal side of an angle after a clockwise rotation of (pi)/(6) radians?