Question 254895
Use a coordinate grid to plot ΔABC with vertices having coordinates A(2,6), B(18,2), C(12,12).  Is this isosceles, right or equilateral?  Where is the midpoint of AB?

{{{drawing(300,200,0,20,0,20,grid(1),triangle( 2, 6, 18, 2, 12, 12 ),locate( 2, 6, A ), locate( 18, 2, B ), locate( 12, 12, C ))}}}

distance = sqrt((x2-x1)^2+(y2-y1)^2)
AB=sqrt((18-2)^2+(2-6)^2)=sqrt(16^2+(-4)^2)=sqrt(256+16)=sqrt(272)=16.49
BC=sqrt((12-18)^2+(12-2)^2)=sqrt((-6)^2+10^2)=sqrt(36+100)=sqrt(136)=11.66
CA=sqrt((2-12)^2+(6-12)^2)=sqrt((-10)^2+(-6)^2)=sqrt(100+36)=sqrt(136)=11.66

not equilateral
is isosceles

right triangle would have AB=sqrt(BC^2+CA^2)
sqrt(BC^2+CA^2)=sqrt(136+136)=sqrt(272)=AB

it is isosceles and a right triangle