Project ForgeEngineering Mathematics
Linear Algebra
GATE 2016
Medium
A triangle PQR has initial vertex coordinates P(1,3), Q(4,5), R(5,3.5). It is rotated in the X-Y plane about vertex P by angle θ in the clockwise direction, with sinθ=0.6, cosθ=0.8. The new coordinates of vertex Q are
- (4.6, 2.8)
- B(3.2, 4.6)
- C(7.9, 5.5)
- D(5.5, 7.9)
Explanation
Relative to P, Q is at (3,2). Clockwise rotation: x'=x cosθ+y sinθ=3(0.8)+2(0.6)=3.6; y'=-x sinθ+y cosθ=-3(0.6)+2(0.8)=-0.2. New Q = P+(x',y') = (1+3.6, 3-0.2) = (4.6, 2.8).
Source: GATE ME 2016 Set-1 (2016)
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