Assertion: If three vertices of a parallelogram ABCD are A (3,-1,2), B (1,2,-4) and C (-1,1,2), then the fourth vertex is (1,-2,8). Reason: Diagonals of a parallelogram bisect each other and mid-point of AC and BD coincide.

Question

Assertion: If three vertices of a parallelogram ABCD are A (3,-1,2), B (1,2,-4) and C (-1,1,2), then the fourth vertex is (1,-2,8). Reason: Diagonals of a parallelogram bisect each other and mid-point of AC and BD coincide. (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

Since diagonals of a parallelogram bisect each other therefore, mid-point of A C and B D coincide. ∴ (1,0,2)=(( x +1/2), ( y +2/2), ( z -4/2)) ⇒ (x+1/2)=1, (y+2/2)=0, (z-4/2)=2 ⇒ x=1, y=-2, z=8

Q. Assertion : If three vertices of a parallelogram $A BC D$ are $A (3, - 1, 2), B (1, 2, - 4)$ and $C (- 1, 1, 2)$ , then the fourth vertex is $(1, - 2, 8)$ .
Reason: Diagonals of a parallelogram bisect each other and mid-point of $A C$ and $B D$ coincide.

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

Since diagonals of a parallelogram bisect each other therefore, mid-point of $A C$ and $B D$ coincide.
$∴ (1, 0, 2) = (\frac{x + 1}{2}, \frac{y + 2}{2}, \frac{z - 4}{2})$
$\Rightarrow \frac{x + 1}{2} = 1, \frac{y + 2}{2} = 0, \frac{z - 4}{2} = 2$
$\Rightarrow x = 1, y = - 2, z = 8$

Q. Assertion : If three vertices of a parallelogram ABCD are A(3,−1,2),B(1,2,−4) and C(−1,1,2), then the fourth vertex is (1,−2,8). Reason: Diagonals of a parallelogram bisect each other and mid-point of AC and BD coincide.