PointHard
Question
The point (4, 1) undergoes the following three transformations successively -
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive directions of x-axis.
(iii) Rotation through an angle π/4 about the origin.
The final position of the point is given by the coordinates :
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive directions of x-axis.
(iii) Rotation through an angle π/4 about the origin.
The final position of the point is given by the coordinates :
Options
A.
B.
C.
D.none of these
Solution
(i) After reflection about the line y = x, (4, 1) becomes (1, 4)
(ii) After 2nd transformation it becomes (3, 4)
(iii) In the 3rd transformation point has been rotated in anticlockwise at an angle of π/4 about origin
∴ its coordinate becomes
(5cos(π/4 + α), 5sin(π/4 + α))
where tan α =
Solving above we can set
the coordinates of final position of the point.
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