Give the equation of two lines passing through (2,10 how many more such lines are there and why)

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Answer

So, from the above figure, if we consider the point as P, we can draw an infinite number of lines passing through the point.

Note: Consider a point in a plane and pass a line through it and we can pass many lines coming from different directions and there is no end to it. The properties of a point also state that infinite lines can pass through the given point.

Text Solution

Solution : Since the given solution is (2,14)<br> ∴x=2 and y=14<br> Then, one equation is <br>x+y=2+14=16 x+y=16<br> And, second equation is <br>x−y=2−14=−12 x−y=−12<br> And, third equation is y=7x<br> 7x−y=0<br> So, we can find infinite equations because through one point infinite lines can pass.

Solution:

Given: Point (2, 14) at which lines passing through.

We can think of framing equations that could satisfy the given point (2, 14) on the line.

It can be observed that point (2, 14) satisfies the equation 7x - y = 0 and x - y + 12 = 0.

Therefore, 7x - y = 0 and x - y + 12 = 0 are two lines passing through point (2, 14).

Since we know infinite lines can pass through a single point, therefore there are infinite more lines passing through the given point

☛ Check: NCERT Solutions Class 9 Maths Chapter 4

Video Solution:

Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.3 Question 2

Summary:

The equations of two lines passing through (2, 14) are 7x − y = 0 and x − y + 12 = 0, there are infinite lines passing through the given point (2, 14).

☛ Related Questions:

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Give the equation of two lines passing through 2,10.

Solution

We have to form equation of two lines passing through (2,10).

i.e., the point (2,10) should satisfies the required equations.

lets observe the sum of the coordinates of the points,

2+10=12

⇒ One of the equation of line is

x+y=12 ---(1)

2−10=−8

⇒ one more equation of the line is

x−y=−8 or y−x=8----(2)

Since, there exist infinite number of lines passing through a point.

we can create the infinite number of equation of lines.

ex:

Point is (2,10)

5(2)−3(10)=10−30=−20

i.e., 5x−3y=−20 is also passing through the point (2,10).