Straight Lines and Pair of Straight Lines Part 1

Both the lines pass through origin point D is equal of intersection of 4x+5y=0 & 11x+7y=9
So, coordinates of point D=(

5

3

,−

4

3

)
Also, point B is point of intersection of 7x+2y=0 & 11x+7y=9
So, coordinates of point B=(−

2

3

,

7

3

)
diagonals of parallelogram intersect at middle let middle point of B,D
⇒(

5 3 − 2 3

2

,

−4

3

+

7

3

)=(

1

2

,

1

2

)
equation of diagonal AC
⇒(y−0)=

1 α −0

1 α −0

(π−0)
y=x
diagonal AC passes through (2, 2).