JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 2 Questions

Given, two sides of parallelogram are
r4x+5y=0
7x+2y=0
‌ and ‌7x+2y=0
Both lines are passing through origin.
Thus, point A=(0,0)
The equation of diagonal is 11x+7y=9
Point D is the point of intersection of
4x+5y=0
and 11x+7y=9
So, coordinate of D=(‌

5

3

,−‌

4

3

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

2

3

,‌

7

3

)
We know that, diagonals of parallelogram bisects each other. Let P is the middle point of BD.

So, coordinate of
P=(‌

‌ 5 3 +(− 2 3 )

2

,‌

− 4 3 + 7 3

2

)=(‌

1

2

,‌

1

2

)
Now, equation of diagonal AC
y−0=‌

‌ 1 2 −0

1 2 −0

(x−0)
⇒y=‌

‌ 1 2

1 2

x⇒y=x
∴ Diagonal AC passes through (2,2).