Answer

Verified

446.7k+ views

**Hint:**Use the given data that $l,m,n$ are in Arithmetic progression, which means that the common difference of each consecutive term is constant, which gives an equation. On comparing the obtained equation with the given equation, we get the required point.

**Complete step-by-step answer:**It is given in the problem that $l,m,n$are in Arithmetic progression and we have to find the point where the lines represented by $lx + my + n = 0$are concurrent.

As given that $l,m,n$ are in Arithmetic progression, it means that the common difference of each congruent term is constant. That is,

$m - l = n - m$

We will simplify the obtained equation by taking the same term of one side.

$ \Rightarrow m + m = n + l$

$ \Rightarrow 2m = n + l$

Now, we shift all the terms on the left-hand side.

$\Rightarrow l - 2m - n = 0$

Now, we compare the above equation with the given equation:

$\Rightarrow lx + my + n = 0$

On comparing both the equation, the coefficient of $l$ given that:

$\Rightarrow x = 1$

On comparing both the equation, the coefficient of $m$ gives that:

$\Rightarrow y = - 2$

So, we have the values $x = 1$and$y = - 2$. Then the obtained point $\left( {x,y} \right)$ is $\left( {1, - 2} \right)$.

Hence, we can see that the line $lx + my + n = 0$ passes through the point $\left( {1, - 2} \right)$. Therefore, the lines represented by $lx + my + n = 0$ are concurrent at the point $\left( {1, - 2} \right)$.

**Hence, option (4) is correct.**

**Note:**The concurrent lines are the lines that intersect at a single point and that point is asking for the question. One line is given to us and one line is formed using the given data, then the point of intersection of these points is the point where the formed lines are concurrent.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you graph the function fx 4x class 9 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE