SATHEE: Straight Line and Pair of Straight Lines 1 Question 69

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 $A D$ .

$∴$ Its equation is of the form $7 x - 4 y + λ = 0$

Since, it passes through $(- 3, 1)$ .

$\begin{aligned} ∴ & 7 (- 3) - 4 (1) + λ & = 0 . \\ \Rightarrow & λ & = 25 \end{aligned}$

$∴$ Equation of $A B$ is

$7 x - 4 y + 25 = 0$

Now, $B C$ is parallel to $A D$ . Therefore, its equation is

$4 x + 7 y + λ = 0$

Since, it passes through $(1, 1)$ .

$\begin{aligned} ∴ & 4 (1) + 7 (1) + λ & = 0 \\ \Rightarrow & λ & = - 11 \end{aligned}$

$∴$ Equation of $B C$ is $4 x + 7 y - 11 = 0$

Now, equation of $D C$ is $7 x - 4 y + λ = 0$

$\begin{aligned} \Rightarrow 7 (1) - 4 (1) + λ = 0 \\ \Rightarrow λ = - 3 \\ ∴ 7 x - 4 y - 3 = 0 \end{aligned}$

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

Answer:

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Straight Line and Pair of Straight Lines 1 Question 69

69. One side of a rectangle lies along the line 4x+7y+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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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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)