How many triangles with positive area can be drawn on the coordinate plane such that the vertices have integer coordinates (x,y) satisfying 1≤x≤3 and 1≤y≤3?
A. 72
B. 76
C. 78
D. 80
E. 84
Can someone please explain this step-by-step and also the logic used behind it?
Thanks so much!!
triangles on coordinate plane - please elaborate
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- neelgandham
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We have exactly 9 points (1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3) to use as vertices.
We can select 3 points from these 9 points in 9C3 ways = 9!/(6!*3!) = 84, of which 8 sets of points result in straight lines. So, 84-8 = 76 triangles with positive area can be drawn on the coordinate plane such that the vertices have integer coordinates (x,y) satisfying 1≤x≤3 and 1≤y≤3?
For detailed solutions by experts click the below links:
https://www.beatthegmat.com/how-many-tri ... 28974.html
https://www.beatthegmat.com/how-many-tri ... 59-15.html
We can select 3 points from these 9 points in 9C3 ways = 9!/(6!*3!) = 84, of which 8 sets of points result in straight lines. So, 84-8 = 76 triangles with positive area can be drawn on the coordinate plane such that the vertices have integer coordinates (x,y) satisfying 1≤x≤3 and 1≤y≤3?
For detailed solutions by experts click the below links:
https://www.beatthegmat.com/how-many-tri ... 28974.html
https://www.beatthegmat.com/how-many-tri ... 59-15.html
Anil Gandham
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