Allied & ICAR Exam Bank • ALLIED_2427MCQ • 2 Marks
Section 8: General Aptitude
Analytical & Spatial Aptitude
Subtopic: Spatial Reasoning & 3D Representations
Question Statement:
A composite shape in the coordinate plane must be symmetric with respect to both coordinate axes (D_2 dihedral symmetry). If the boundary in Quadrant I is given by the curve y = 4 - x^2 for x in [0, 2], what is the equation of the boundary in Quadrant III?
Options:
(A) y = -(4 - (-x)^2) = x^2 - 4 for x in [-2, 0]
(B) y = 4 - x^2 for x in [-2, 0]
(C) y = x^2 + 4 for x in [-2, 0]
(D) y = -4 - x^2 for x in [-2, 0]
Answer Key:
A
Step-by-Step Solution & Explanation
Reflecting across both axes maps (x, y) to (-x, -y). Substituting: -y = 4 - (-x)^2 = 4 - x^2, so y = x^2 - 4 for x in [-2, 0].