The point (4, 1) undergoes the following three transformations successively
I. Reflection about the line .
II. Transformation through a distance 2 units along the positive direction of X-axis.
III. Rotation through an angle about the origin in the counter clockwise direction.
Then, the final position of the point is given by the coordinates
I. Reflection about the line .
II. Transformation through a distance 2 units along the positive direction of X-axis.
III. Rotation through an angle about the origin in the counter clockwise direction.
Then, the final position of the point is given by the coordinates
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: C
Solution
After reflection about y = x: (4,1) → (1,4).
After translation 2 units along positive x-axis: (1,4) → (3,4).
After rotation by π/4 counterclockwise: new coordinates are (x cosθ - y sinθ, x sinθ + y cosθ) = (3·(1/√2) - 4·(1/√2), 3·(1/√2) + 4·(1/√2)) = (-1/√2, 7/√2).
After translation 2 units along positive x-axis: (1,4) → (3,4).
After rotation by π/4 counterclockwise: new coordinates are (x cosθ - y sinθ, x sinθ + y cosθ) = (3·(1/√2) - 4·(1/√2), 3·(1/√2) + 4·(1/√2)) = (-1/√2, 7/√2).
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