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The equations of two sides of a triangle...

The equations of two sides of a triangle are `3y-x-2=0a n dy+x-2=0.` The third side, which is variable, always passes through the point `(5,-1)` . Find the range of the values of the slope of the third side, so that the origin is an interior point of the triangle.

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We have two sides of triangle as 3x-x-2=0 and y+x-2=0.
The third side is passing through the point A(5,-1).
Different lines through point A are drawn as shown in the following figure.

Line `L_(2)` through A is parallel to the line x-3y+2=0, which has slope 1/3.
In this case, triangle is not formed.
Line `L_(1)` through A goes through origin, which has slope -1/5.
In this case triangle is formed but origin lies on the side of the triangle.
Line `L_(3)` through A is such that triangle is formed and origin lies inside the triangle.
Thus, required values of slope of line are (-1/5,1/3).
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