Straight Line and Pair of Straight Lines 1 Question 69
69. One side of a rectangle lies along the line $4 x+7 y+5=0$. Two of its vertices are $(-3,1)$ and $(1,1)$. Find the equations of the other three sides. (1978, 3M)
Integer Answer Type Question
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Answer:
Correct Answer: 69. 6 sq units
Solution:
- Since, the side $A B$ is perpendicular to $A D$.
$\therefore$ Its equation is of the form $7 x-4 y+\lambda=0$
Since, it passes through $(-3,1)$.
$$ \begin{aligned} \therefore & & 7(-3)-4(1)+\lambda & =0 . \\ & \Rightarrow & \lambda & =25 \end{aligned} $$
$\therefore$ Equation of $A B$ is
$$ 7 x-4 y+25=0 $$
Now, $B C$ is parallel to $A D$. Therefore, its equation is
$$ 4 x+7 y+\lambda=0 $$
Since, it passes through $(1,1)$.
$$ \begin{aligned} \therefore & & 4(1)+7(1)+\lambda & =0 \\ \Rightarrow & & \lambda & =-11 \end{aligned} $$
$\therefore$ Equation of $B C$ is $\quad 4 x+7 y-11=0$
Now, equation of $D C$ is $7 x-4 y+\lambda=0$
$$ \begin{aligned} & \Rightarrow \quad 7(1)-4(1)+\lambda=0 \\ & \Rightarrow \quad \lambda=-3 \\ & \therefore \quad 7 x-4 y-3=0 \end{aligned} $$
