Question

Three vertices of a parallelogram PQRS taken in order are P(3, 6), Q(5, 10) and R(3, 2). Find: (i) the co-ordinates of S (ii) Length of diagonal QS.​

Answer 1

Step-by-step explanation:

Let A(1,−2), B(3,6) and C(5,10) be the three vertices of a parallelogram ABCD and let its fourth vertex be D(a,b).

Join AC and BD. Let AC and BD intersect at point O.

We know that the diagonals of a parallelogram bisect each other.

So, O is the midpoint of AC as well as that of BD.

Using Midpoint formula X=(

2

x

1

+x

2

)and Y=(

2

y

1

+y

2

)

A(1,−2)≡(x

1

,y

1

), C(5,10)≡(x

2

,y

2

)

Midpoint of AC is (

2

1+5

,

2

−2+10

), i.e.,(3,4)

Midpoint of BD is (

2

3+a

,

2

6+b

)

∴

2

3+a

=3 and

2

6+b

=4

3+a=6 and 6+b=8

a=3 and b=2

Hence, the fourth vertex is D(3,2).

Answer 2

Step-by-step explanation:

today it was a boring today for me i was alone in the class room i was getting headache. so i slept for a two periods i missed my activity class and music class but when  suddenly i heard an un natural sound i got up and saw what was happening i sawed that two dangerous looking men in the class room they were those two men whom they were showing in tv as most wanted i ran out from class room i informed to my principal he quickly informed the police and till the time police came our principal said to vacant the school  police came after some time they announced that if they dont come out they will blast the school they came and surrendered themself the police commisnor awarded me