Question

Assertion :The quadrilateral whose vertices (in order) are $A\equiv (1,0)$, $B\equiv (0,3)$, $C\equiv (-2,0)$ and $D\equiv (0,2)$ can not be convex. Reason: A quadrilateral $ABCD$ (in order) is convex if and only if when any diagonal is taken then the remaining vertices must be on the opposite sides of it.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

The reason is correct because if one angle e.g. D of the quadrilateral ABCD which is not convex is more than ${180}^{\circ }$ then B and D lie on the same side of the diagonal AC of the quadrilateral.

The reason states that when a diagonal is drawn from any two vertices, then the other two vertices must lie on the opposite sides of it.

From the given figure, if the diagonal BD is considered, then points $A$ and $C$ lie on the same side.

Thus, the reason is correct for the given statement.