Assertion: If A(-2,-1), B(4,0), C(3,3) and D(-3,2) are the vertices of a parallelogram, then mid-point of AC = Mid-point of BD Reason: The points A , B and C are collinear Leftrightarrow Area of Δ ABC =0

Question

Assertion: If A(-2,-1), B(4,0), C(3,3) and D(-3,2) are the vertices of a parallelogram, then mid-point of AC = Mid-point of BD Reason: The points A , B and C are collinear Leftrightarrow Area of Δ ABC =0 (A) Assertion is correct, reason is correct; reason is a correct explanation for assertion. (B) Assertion is correct, reason is correct; reason is not a correct explanation for assertion (C) Assertion is correct, reason is incorrect (D) Assertion is incorrect, reason is correct.

Tardigrade Admin · Accepted Answer

Mid-point of AC =((1/2), (2/2)) =((1/2), 1) Mid-point of BD =((1/2), 1)

Q. Assertion: If $A (- 2, - 1), B (4, 0), C (3, 3)$ and $D (- 3, 2)$ are the vertices of a parallelogram, then mid-point of $A C =$ Mid-point of $B D$
Reason: The points $A, B$ and $C$ are collinear $\Leftrightarrow$ Area of $Δ A BC = 0$

Assertion is correct, reason is correct; reason is a correct explanation for assertion.

Assertion is correct, reason is correct; reason is not a correct explanation for assertion

Assertion is correct, reason is incorrect

Assertion is incorrect, reason is correct.

Mid-point of $A C = (\frac{1}{2}, \frac{2}{2})$
$= (\frac{1}{2}, 1)$
Mid-point of $B D = (\frac{1}{2}, 1)$

Q. Assertion: If A(−2,−1),B(4,0),C(3,3) and D(−3,2) are the vertices of a parallelogram, then mid-point of AC= Mid-point of BD Reason: The points A,B and C are collinear ⇔ Area of ΔABC=0