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

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

Straight Line and Pair of Straight Lines 3 Question 1

1.

Answer:

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Straight Line and Pair of Straight Lines 3 Question 1

1.

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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