(1,1) ( 4,4) ( 5,-1)
First we need to find the lengths of the sides
( 1,1) ( 4,4)
length = sqrt( ( 4-1) ^2 + ( 4-1) ^2)
length = sqrt( 3^2 + 3^2) = sqrt(18) = 2 sqrt(3)
(4,4) ( 5,-1)
length = sqrt( ( 5-4) ^2 + ( -1 -4) ^2 )
length = sqrt( 1^2 + ( -5) ^2) = sqrt( 1+25) = sqrt( 26)
(5,-1) ( 1,1)
length = sqrt( ( 1-5) ^2 + ( 1 - -1) ^2)
length = sqrt( ( -4) ^2 + 2^2) = sqrt( 16 +4) = sqrt(20)
To determine if it is right obtuse or acute, we use
a^2 + b^2 c^2
if > acute
= right
< obtuse
( sqrt(18))^2+ ( sqrt(20))^2 (sqrt( 26))^2
18+20 > 26 so this is acute
You do the same procedure for the other 2 triangles
(1,2) ( 4,4) ( 6,3) will be obtuse
(2,3) (4,4) (5,2) will be right