Answer:
[tex]\text{Solution:}\\\text{Let A(2,4), B(6,4) and C(6,7) form a right triangle ABC.}\\\\\text{From distance formula,}\\\text{AB}^2=(6-2)^2+(4-4)^2=4^2\\\text{BC}^2=(6-6)^2+(7-4)^2=3^2\\\text{AC}^2=(6-2)^2+(7-4)^2=4^2+3^2\\[/tex]
[tex]\text{Here, since }\text{AC}^2=\text{AB}^2+\text{BC}^2,\text{ the pythagoras theorem is satisfied.}\\\text{Therefore, triangle ABC is right angled triangle.}[/tex]
[tex]\text{In this triangle, AC will be hypotenuse (side opposite to right angle) and}\\\text{AB and BC will be the other legs.}[/tex]
