SOLUTION: show how three lines in a plane can intersect in no points,exactly one point ,exactly two points or exactly three points

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Question 118848This question is from textbook discovering geometry an investigative approach
: show how three lines in a plane can intersect in no points,exactly one point ,exactly two points or exactly three points This question is from textbook discovering geometry an investigative approach

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Intersect at NO points ... make the three lines parallel (all having the same slope) as shown below:
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graph%28400%2C400%2C0%2C20%2C0%2C20%2C2x-6%2C+2x%2C+2x+%2B+6%29
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Intersect at ONE point ... make the three lines cross at a single point and all have different slopes
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graph%28400%2C400%2C0%2C20%2C0%2C20%2C2x%2C+4x-10%2C+-3x%2B25%29
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Intersect at exactly TWO points ... make two of the lines parallel and one a transversal that
cuts across them:
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graph%28400%2C400%2C0%2C20%2C0%2C20%2C2x-4%2C+2x%2B6%2C+-2x+%2B+19%29
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Intersect at exactly THREE points ... make the three lines form a triangle.
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graph%28400%2C400%2C0%2C20%2C0%2C20%2Cx%2B5%2C+3x%2C+-x+%2B+19%29
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Hope this helps you to visualize the answers the problem was asking you to document.
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