Assertion (A): If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram (in order), then p = 7

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Q.
Assertion (A): If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram (in order), then p = 7.

Reason (R): Diagonals of a parallelogram bisect each other, therefore midpoint of AC = midpoint of BD.

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false.

4 A is false, but R is true

Ans.
(1)

Given ABCD is a parallelogra, Diagonals bisect each other, so

$Midpoint of A C = Midpoint of B D (\frac{6 + 9}{2}, \frac{1 + 4}{2}) = (\frac{p + 8}{2}, \frac{3 + 2}{2}) S i m p l i f y i n g : (\frac{15}{2}, \frac{5}{2}) = (\frac{p + 8}{2}, \frac{5}{2}) C o m p a r i n g x - c o o r d i n a t e s : \frac{15}{2} = \frac{p + 8}{2} p + 8 = 15 \Rightarrow p = 7$

Solution

Q.
Assertion (A): If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram (in order), then p = 7.

Reason (R): Diagonals of a parallelogram bisect each other, therefore midpoint of AC = midpoint of BD.

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false.

4 A is false, but R is true

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Solution

Q. Assertion (A): If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram (in order), then p = 7. Reason (R): Diagonals of a parallelogram bisect each other, therefore midpoint of AC = midpoint of BD.

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false.

4 A is false, but R is true

Ans. (1) Given ABCD is a parallelogra, Diagonals bisect each other, so Midpoint of AC=Midpoint of BD(6+92,1+42)=(p+82,3+22)Simplifying:(152,52)=(p+82,52)Comparing x-coordinates:152=p+82p+8=15⇒p=7

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Q.
Assertion (A): If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram (in order), then p = 7.

Reason (R): Diagonals of a parallelogram bisect each other, therefore midpoint of AC = midpoint of BD.