Student: Vaishnavi Gupta

Q. Give the equations of two lines passing through (2, 14). Calculate how many more such lines are there also give reason?


Answer :

Hi Vaishnavi,  Thanks for your query. 

Topic: Geometry, Equation of line

Core Concept:
The Greek Mathematician of Euclid`s time derived the notion of point, line, plane etc. from what they have seen around them. They thought of Geometry as an abstract model of world they lived in.

From studies of the space and solids in the space around them, an abstract geometrical notion of a solid object was developed.
 

Consider the three steps from solids to points (solids-surfaces-lines-points). In each step we lose one extension, also called a dimension. So, a solid has three dimensions, a surface has two, a line has one and a point has none.

Euclid summarized these statements as definitions.

  • A point is that which has no part.
  • A line is breadthless length.

As per Euclid`s Axioms :  Point is that which has no part.
So there can be infinite number of  lines passing through a given point as you can visibly see also.

Method and Solution :
Given the point (2,14), there can be infinite lines passing through it. Here are two examples  of equation of lines as you have asked:
         y-x=12 
         x+y = 16


More Examples : 
       2x+y= 18 
       9x-y=4 
       7x-y=0 
Idea is that the given point shall satisfy the equation.

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