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avatar+138 

How many different isosceles right triangles can be formed from three dots in the grid below? Two examples are shown.

[asy]
unitsize(0.8 cm);

int i, j;

draw((0,1)--(1,2)--(0,2)--cycle,red);
draw((0,0)--(2,0)--(2,2)--cycle,blue);

for (i = 0; i <= 2; ++i) {
for (j = 0; j <= 2; ++j) {
dot((i,j),linewidth(5*bp));
}}
[/asy]

 

( 3x3 dot grid )

 Feb 11, 2020
edited by Forumofweb2.0cal  Feb 11, 2020
 #1
avatar
0

There are triangles with side lengths 1, 1, sqrt(2) and 2, 2, 2*sqrt(2).  So there are a total of 12 + 4 = 16 triangles.

 Feb 11, 2020
 #2
avatar+138 
-1

It was incorrect

 Feb 11, 2020
 #3
avatar
0

There are actually 16 triangles of the first kind, so the answer is 16 + 4 = 20.

 Feb 13, 2020

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