Straight LineMedium
Question
The poinr (4, 1) undergoes the following three transformations successively
(I) Reflection about the line y = x
(II) Transformation through a distance 2 unit along the poitive direction of x-axis.
(III) Rotation through an angle
about the origin in the counter clockwise dirction.Then, the final position of the point is given by the coordinates
(I) Reflection about the line y = x
(II) Transformation through a distance 2 unit along the poitive direction of x-axis.
(III) Rotation through an angle
about the origin in the counter clockwise dirction.Then, the final position of the point is given by the coordinatesOptions
A.
B.(- √2, 7√2)
C.
D.(√2, 7√2)
Solution
Let B, C, D be the position of the point A (4, 1) after the three operations I, II and III respec tively. Then, B is (1, 4), C (1 + 2, 4) ie, (3, 4). The point D is obtained from C by rotating the coordinate axes through an angle π / 4 in anticlockwise direction.
Therefore, the coordinates of D are given by
and
∴ Coordinates of D are
Therefore, the coordinates of D are given by
and
∴ Coordinates of D are
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