Question

Area of the quadrilateral formed by the lines 4y
- 3x - a=0,3y - 4x+a=0, 4y - 3x - 3a=0, 3y -
4x+2a=0 is​

Answer 1

Answer:

Step-by-step explanation:

We have,

4x−3x−a=0 ---(1)

3y−4x+a=0 ---(2)

4y−3x−3a=0 ---(3)

3y−4x+2a=0 ---(4)

4y−3a−a=0 and 3y−4x+a=0

4x−3x−3a=0 3y−4x+2a=0

So,

m  

1

​  

=  

4

3

​  

 m  

2

​  

=  

3

4

​  

 

Perpendicular distance perpendicular distance between these lines

Between this lines=  

∣

∣

∣

∣

∣

​  

 

5

2a

​  

 

∣

∣

∣

∣

∣

​  

 =  

∣

∣

∣

∣

​  

 

5

a

​  

 

∣

∣

∣

∣

​  

 

From 1 & 2, From 1& 4,

y=a,x=a y=  

7

10

​  

a,x=  

7

11

​  

a

AB=  

7

5a

​  

 

So, area of parallelogram formed is h×b

=  

7

5a

​  

×  

5

2a

​  

=  

7

2a  

2

 

​