nolenat2
Answered

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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:

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