SATHEE: Straight Line and Pair of Straight Lines 3 Question 1

Straight Line and Pair of Straight Lines 3 Question 1

1. A triangle has a vertex at $(1, 2)$ and the mid-points of the two sides through it are $(- 1, 1)$ and $(2, 3)$ . Then, the centroid of this triangle is

(2019 Main, 12 April II)

(a) $1, \frac{7}{3}$

(b) $\frac{1}{3}, 2$

(d) $\frac{1}{3}, \frac{5}{3}$

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Answer:

Correct Answer: 1. (b)

Solution:

Let a $△ A B C$ is such that vertices

$A (1, 2), B (x_{1} y_{1})$ and $C (x_{2}, y_{2})$ .

It is given that mid-point of side $A B$ is $(- 1, 1)$ .

$\begin{array}{lc} So, & \frac{x_{1} + 1}{2} = - 1 \\ and & \frac{y_{1} + 2}{2} = 1 \\ \Rightarrow & x_{1} = - 3 and y_{1} = 0 \end{array}$

So, point $B$ is $(- 3, 0)$

Also, it is given that mid-point of side $A C$ is $(2, 3)$ , so

$\begin{aligned} \frac{x_{2} + 1}{2} & = 2 and \frac{y_{2} + 2}{2} = 3 \\ \Rightarrow & x_{2} & = 3 and y_{2} = 4 \end{aligned}$

So, point $C$ is $(3, 4)$ .

Now, centroid of $△ A B C$ is

$G \frac{1 + (- 3) + 3}{3}, \frac{2 + 0 + 4}{3} = G \frac{1}{3}, 2$

2 Given, $p x + q y + r = 0$ is the equation of line such that $3 p + 2 q + 4 r = 0$

$\begin{aligned} Consider, & 3 p + 2 q + 4 r & = 0 \Rightarrow & \underset{―}{3 p} + \underset{―}{2 q} + r = 0 \end{aligned}$

$\Rightarrow \frac{3 p}{4} + \frac{2 q}{4} + r = 0$

$\Rightarrow p \frac{3}{4} + q \frac{1}{2} + r = 0$

$\Rightarrow \frac{3}{4}, \frac{1}{2}$ satisfy $p x + q y + r = 0$

So, the lines always passes through the point $\frac{3}{4}, \frac{1}{2}$ .

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Straight Line and Pair of Straight Lines 3 Question 1

1. A triangle has a vertex at $(1, 2)$ and the mid-points of the two sides through it are $(- 1, 1)$ and $(2, 3)$ . Then, the centroid of this triangle is

Answer:

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Straight Line and Pair of Straight Lines 3 Question 1

1. A triangle has a vertex at (1,2) and the mid-points of the two sides through it are (−1,1) and (2,3). Then, the centroid of this triangle is

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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1. A triangle has a vertex at $(1, 2)$ and the mid-points of the two sides through it are $(- 1, 1)$ and $(2, 3)$ . Then, the centroid of this triangle is