nolenat2
Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

The coordinate plane shows three vertices of a parallelogram. Which are two possible points that could represent the fourth vertex?(6,2) ( 6 , 2 ) and (8,8) ( 8 , 8 ) , (5,1) ( 5 , 1 ) and (8,1) ( 8 , 1 ), (6,1) ( 6 , 1 ) and (8,9) ( 8 , 9 ) , (8,1), ( 8 , 1 ) and (6,9)

Sagot :

Answer:

Solution

Correct option is A)

Sol. 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).

Step-by-step explanation:

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.