SOLUTION: 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?

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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?
Answer by CharlesG2(834) About Me  (Show Source):
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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?

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