Question

If( 2,9),(-2,1) and (1,-3)are the vertices of a triangle then prove that the origin lies inside the triangle

Answer 1

points 2,9),(-2,1) and (1,-3) lie in quadrants 1,2and3 respectively
for any triangle formed from the three points lying in three different quadrants, the origin lies inside the triangle

Answer 2

If (2, 9), (-2, 1), and (1,-3) are the vertices of a triangle then the origin lies inside the triangle.

Given:  

(2, 9), (-2, 1), and (1, -3) are the vertices of a triangle  

To find:

Prove that the origin lies inside the triangle  

Solution:

Given vertices of the triangle are (2, 9), (-2, 1), and (1, -3)  

Plot the given vertices in a coordinate plane  

We can observe that

The vertices (2, 9) lie in the 1st Quadrant  

The vertices (-2, 1) lie in the 2nd Quadrant

The vertices (1, -3) lie in the 4th Quadrant

Here 3 vertices are in 3 different quadrants which include the origin  

[ For more understanding observe the given picture ]  

Hence we can conclude that in the given triangle the origin will lie inside the triangle

Therefore,

If (2, 9), (-2, 1), and (1,-3) are the vertices of a triangle then the origin lies inside the triangle.

   

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