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

SmartMathMan
Jan 19, 2018

#1**+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....!!!!!

CPhill
Jan 19, 2018