Answer
Yes, $(5,7)$
Work Step by Step
Step 1. Given $A(5,7), B(3,9)$, the distance between the points is $d(A,B)=\sqrt {(5-3)^2+(7-9)^2}=2\sqrt {2}$
Step 2. Given $B(3,9), C(6,8)$, the distance between the points is $d(B,C)=\sqrt {(6-3)^2+(8-9)^2}=\sqrt {10}$
Step 3. Given $A(5,7), C(6,8)$, the distance between the points is $d(A,C)=\sqrt {(6-5)^2+(8-7)^2}=\sqrt 2$
Step 4. Since $(d(B,C))^2=(d(A,B))^2+(d(A,C))^2$, based on the Pythagorean theorem, the three points form a right triangle with point $A(5,7)$ being the right angle
