Question

If A(2,-1) B(5,1) C(5,6) D(2,6) are the vertices of a square then coordinates of the intersecting point of its diagonals is​

Answer 1

Answer:

We know that the diagonals of a parallelogram bisect each other. So, coordinates of the mid-point of diagonal AC are same as the coordinates of the mid-point of diagonal BD.

∴(  

2

6+9

​

,  

2

1+4

​

)=(  

2

8+p

​

,  

2

2+3

​

)

⇒(  

2

15

​

,  

2

5

​

)=(  

2

8+p

​

,  

2

5

​

)

⇒  

2

15

​

=  

2

8+p

​

⇒15=8+p⇒p=7

Step-by-step explanation:

Answer 2

Answer:

The answer is (7/2,5/2)

Step-by-step explanation:

1. As given in the equation there is a square. let the square be abcd where each vertices have the values given in the equation

2.we know that the vertices of the squares are A(2,-1) B(5,1) C(5,6) D(2,6)

3. there are 2 diagonals . let them be ac and bd

4. let both the diagonals intersect at 0.

6. diagonals of a square bisect each other.

7. let us have 4 points in ac diagonal

8. x1= 2 , y1=-1

9. x2=5,y2=1

by using the midpoint theorem we get

Midpoint Formula $M (x, y) = [½(x1 + x2), ½(y1 + y2)]$

where $x1=2, y1=-1$

           $x2=5 , y1=5$

implementing the numbers in the equation we get

hence the answer is

$0(x,y) = (2+5/2,-1+6/2)\\\\(x,y)= (7/2 , 5/2)$

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