Question 129831
You can find distances

d(C,A)=sqrt(4^2+1^2)=sqrt(17)
d(C,B)=sqrt(2^2+8^2)=sqrt(68)
d(A,B)=sqrt(6^2+7^2)=sqrt(85)

then d(A,B)^2=d(C,A)^2+d(C,B)^2 ehen using Pythagoras Theorem
triangle ABC is a right angled triangle in C

(You can also find lines AC and BC and verify they form a right angle)