SATHEE: Straight Line and Pair of Straight Lines 3 Question 3

Straight Line and Pair of Straight Lines 3 Question 3

4. Area of the parallelogram formed by the lines $y = m x, y = m x + 1, y = n x$ and $y = n x + 1$ equals

(a) $\frac{| m + n |}{(m - n)^{2}}$

(b) $\frac{2}{| m + n |}$

(d) $\frac{1}{| m - n |}$

(2001, 1M)

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Answer:

Correct Answer: 4. (d)

Solution:

Let lines $O B : y = m x$

$\begin{aligned} C A : y & = m x + 1 \\ B A : y & = n x + 1 \\ and O C : y & = n x \end{aligned}$

The point of intersection $B$ of $O B$ and $A B$ has $x$ coordinate $\frac{1}{m - n}$ .

Now, area of a parallelogram $O B A C$

$\begin{aligned} = 2 \times area of △ O B A \\ = 2 \times \frac{1}{2} \times O A \times D B = 2 \times \frac{1}{2} \times \frac{1}{m - n} \\ = \frac{1}{m - n} = \frac{1}{| m - n |} \end{aligned}$

depending upon whether $m > n$ or $m < n$ .

Straight Line and Pair of Straight Lines 3 Question 3

4. Area of the parallelogram formed by the lines $y = m x, y = m x + 1, y = n x$ and $y = n x + 1$ equals

Answer:

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Straight Line and Pair of Straight Lines 3 Question 3

4. Area of the parallelogram formed by the lines y=mx,y=mx+1,y=nx and y=nx+1 equals

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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4. Area of the parallelogram formed by the lines $y = m x, y = m x + 1, y = n x$ and $y = n x + 1$ equals