MHTCET 16 Apr 2026 Shift 1 Paper

Concept:A quadrilateral with both pairs of opposite sides equal and parallel is a parallelogram.Check adjacent sides for equal length (rhombus) and perpendicularity (rectangle).Explanation:The position vectors give the coordinates:$$A(-2,-1), \quad B(4,0), \quad C(3,3), \quad D(-3,2).$$Find the side vectors:$$\overrightarrow{AB} = (6,1), \quad \overrightarrow{DC} = (6,1),$$$$\overrightarrow{BC} = (-1,3), \quad \overrightarrow{AD} = (-1,3).$$Both pairs of opposite sides are equal and parallel, so $ABCD$ is a parallelogram.Now check adjacent sides:$$|AB| = \sqrt{6^2 + 1^2} = \sqrt{37},$$$$|BC| = \sqrt{(-1)^2 + 3^2} = \sqrt{10}.$$Since $\sqrt{37} \neq \sqrt{10}$, adjacent sides are not equal, so it is not a rhombus.Check perpendicularity using dot product:$$\overrightarrow{AB} \cdot \overrightarrow{BC} = (6)(-1) + (1)(3) = -3 \neq 0.$$Adjacent sides are not perpendicular, so it is not a rectangle.Therefore, $ABCD$ is a parallelogram which is neither a rhombus nor a rectangle.Answer:Option A — a parallelogram which is neither a rhombus nor a rectangle.