Question

three consecutive vertices of parallelogram (3,0);(5,2);(-2,6) find the fourth vertex​

Answer 1

Answer:

We have,

A(x

1

​

,y

1

​

)=(3,0)

B(x

2

​

,y

2

​

)=(5,2)

C(x

3

​

,y

3

​

)=(−2,6)

Let AC be the diagonal of rectangle

Then,

Let middle point of Diagonal is (x,y)

(x,y)=

2

x

1

​

+x

3

​

​

,

2

y

1

​

+y

3

​

​

(x,y)=(

2

3+(−2)

​

,

2

0+6

​

)

(x,y)=(

2

1

​

,3)

Let the fourth vertex of rectangle is D and its coordinate is (x

4

​

,y

4

​

)

So, BD is the diagonal of its rectangle.

Then,

(x,y)=(

2

x

2

​

+x

4

​

​

,

2

y

2

​

+y

4

​

​

)

(

2

1

​

,3)=(

2

5+x

4

​

​

,

2

2+y

4

​

​

)

2

1

​

=

2

5+x

4

​

​

,3=

2

2+y

4

​

​

5+x

4

​

=1,6=2+y

4

​

x

4

​

=−4,y

4

​

=4

Hence, the fourth vertices is find

This is a rectangle.

Step-by-step explanation: