Project ForgeEngineering Mathematics
Linear Algebra
GATE 2013
Medium
In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the transformed point will be
- A(7.5, 5)
- (10, 5)
- C(7.5, −5)
- D(10, −5)
Explanation
Reflection about a line through the origin at angle θ to the X-axis is given by the matrix [[cos2θ, sin2θ],[sin2θ, −cos2θ]]. For θ=45°, 2θ=90°, so the matrix is [[0,1],[1,0]] — this simply swaps the coordinates. Applied to (5,10): the transformed point is (10, 5).
Source: GATE ME 2013 (Booklet Code A) (2013)
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