Question

In a rhombus ABCD, 1. 2. 3.

Answer 1

Answer:

Thus, the equation of BD is x+y=5

Step-by-step explanation:

Given, ABCD is a rhombus and co-ordinates of A are (3,6) and of C are (−1,2)

Slope of AC(m  

1

​

)=  

(−1−3)

(2−6)

​

=  

−4

−4

​

=1

We know that, the diagonals of a rhombus bisect each other at the right angles.

So, the diagonal BD is perpendicular to diagonal AC

Let the slope of BD be m  

2

​

 

Then, m  

1

​

×m  

2

​

=−1

m  

2

​

=  

(m  

1

​

)

−1

​

 

=  

(−1)

−1

​

=−1

Now, the co-ordinates of the mid- point of AC is given by

(  

2

(3−1)

​

,  

2

(6+2)

​

)=(  

2

2

​

,  

2

8

​

)=(1,4)

So, the equation of BD will be

y−4=−1(x−1)

y−4=−x+1

x+y=5

Thus, the equation of BD is x+y=5

Answer 2

Answer:

Hope it's correct

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