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How many rectangles are there whose four vertices are points on this 3 by 3 grid?

 

 

 Jan 19, 2018
edited by SmartMathMan  Jan 19, 2018
 #1
avatar+98005 
+2

I count 9

 

BTW  ....

 

There is actually a   formula for the total number of rectangles  [ including squares ] on a N x N   grid  :

 

[ Here......"grid" refers to  N squares by N squares...so....using this definition, you have a 2 x 2 grid ] 

 

(N)^2  ( N + 1)^2   /  4   =    (2)^2 * (3)^2  / 4  =   4 * 9  /  4   =   36 / 4    =   9   

 

 

EDIT......as hectictar points out....there is also an additional square created by connecting the "mid-point"   vertices of each side....so.....the correct answer seems to be 10....!!!!!

 

cool cool cool

 Jan 19, 2018
edited by CPhill  Jan 20, 2018
 #2
avatar+17163 
+2

Good call Hectictar !     10   !      I also answered 9 earlier .....

 Jan 20, 2018

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