SATHEE: Straight Line and Pair of Straight Lines 1 Question 67

Straight Line and Pair of Straight Lines 1 Question 67

67. The points $(1, 3)$ and $(5, 1)$ are two opposite vertices of a rectangle. The other two vertices lie on the line $y = 2 x + c$ . Find $c$ and the remaining vertices. (1981,4M)

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Answer:

Correct Answer: 67. $(- 4, - 7)$

Solution:

Since, diagonals of rectangle bisect each other, so mid point of $(1, 3)$ and $(5, 1)$ must satisfy $y = 2 x + c$ , i.e. $(3, 2)$ lies on it.

$\Rightarrow c = - 4$

$∴$ Other two vertices lies on $y = 2 x - 4$

Let the coordinate of $B$ be $(x, 2 x - 4)$ .

$∴$ Slope of $A B \cdot$ Slope of $B C = - 1$

$\begin{aligned} \Rightarrow \frac{2 x - 4 - 3}{x - 1} \cdot \frac{2 x - 4 - 1}{x - 5} = - 1 \\ \Rightarrow (x^{2} - 6 x + 8) = 0 \\ \Rightarrow x = 4, 2 \\ \Rightarrow y = 4, 0 \end{aligned}$

Hence, required points are $(4, 4), (2, 0)$ .

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Straight Line and Pair of Straight Lines 1 Question 67

67. The points $(1, 3)$ and $(5, 1)$ are two opposite vertices of a rectangle. The other two vertices lie on the line $y = 2 x + c$ . Find $c$ and the remaining vertices. (1981,4M)

Answer:

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Straight Line and Pair of Straight Lines 1 Question 67

67. The points (1,3) and (5,1) are two opposite vertices of a rectangle. The other two vertices lie on the line y=2x+c. Find c and the remaining vertices. (1981,4M)

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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67. The points $(1, 3)$ and $(5, 1)$ are two opposite vertices of a rectangle. The other two vertices lie on the line $y = 2 x + c$ . Find $c$ and the remaining vertices. (1981,4M)