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All points lying inside the triangle formed by the points (1,3),(5,0) and (-1,2) will satisfy relation--a) 3x+2y>_0 b) 2x+y-13 >_0c) 2x-3y-12 _0

All points lying inside the triangle formed by the points (1,3),(5,0) and (-1,2) will satisfy relation--a) 3x+2y>_0 b) 2x+y-13 >_0c) 2x-3y-12 _0

Grade:11

4 Answers

Arun
25750 Points
6 years ago
Dear Lucky
 
 

If all the three vertices of a triangle lie on one side of a line , all the interior points of that triangle lie on the same side of that line. 

Now, Substituting the coordinates of the points (1,3), (5,0) and (-1,2) in 3x+2y, we get the following values, 

8,15 and 1 which all are +ve.

therefore, all the points lying inside the triangle formed by given points satisfy 

3x+2y >= 0 

In the same way, all the points lying inside the triangle formed by given points also satisfy 

2x-3y-12

 

 

Regards

Arun (askIITians forum expert)

Lucky
27 Points
6 years ago
Thank you sir, I really got struck with that problem.now I get how to think for such type of questions
Samuel Garry
61 Points
5 years ago
Is anybody having a better approach to deal with these types of questions can't we just take out specific equation of lines of family of lines which can be done by solving not just checking by the options
Aur in this question we have to check the answers just by putting them in options
Prakhar Mani Tripathi
13 Points
5 years ago
We can even check by position of a point with reapect to a line concept
Firstly plot the points rougly to get the idea that a point should be above or below the 3 sides of the triangle(you need to take out that) and get the required condition without the options. ....

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