JEE Advance - Mathematics (1980 - No. 19)
The point $$\,\left( {4,\,1} \right)$$ undergoes the following three transformations successively.
Reflection about the line $$y=x$$.
Translation through a distance 2 units along the positive direction of x-axis.
Rotation through an angle $$p/4$$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.
Reflection about the line $$y=x$$.
Translation through a distance 2 units along the positive direction of x-axis.
Rotation through an angle $$p/4$$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.
$$\left( {{1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$$
$$\left( { - \sqrt 2 ,\,7\sqrt 2 } \right)$$
$$\left( { - {1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$$
$$\left( { \sqrt 2 ,\,7\sqrt 2 } \right)$$