The point undergoes the following three transformations successively: (i) reflection about the line (ii) Transformation through a distance unit along the positive direction of x-axis (iii) rotation through an angle of about the origin in the anticlockwise direction. The final position of the point is given by the coordinates.

Explanation: Step 1: Reflection about the line When a point is reflected about the line , the coordinates are swapped. Let the new point be . Step 2: Translation by units along the positive x-axis To move a point along the positive x-axis, we add the distance to the x-coordinate. Let the new point be . Step 3: Rotation through ( ) anticlockwise about the origin The formula for rotation of a point by an angle is: Given , , and : Calculating the new coordinates : Conclusion: The final coordinates are . Correct Option: (a)

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NIMCET 2010 — Mathematics PYQ

NIMCET | Mathematics | 2010

The point $(4, 1)$ undergoes the following three transformations successively:

(i) reflection about the line $y = x$

(ii) Transformation through a distance $2$ unit along the positive direction of x-axis

(iii) rotation through an angle of $\pi / 4$ about the origin in the anticlockwise direction.

The final position of the point is given by the coordinates.

Choose the correct answer: