Answer
Triangle ABC satisfy the Pythagoras theorem.
Therefore triangle ABC is a right triangle.
Work Step by Step
By using distance formula
AC = $\sqrt (a-0)^{2} + (b-0)^{2}$ = $\sqrt a^{2} + b^{2}$
AB = $\sqrt (a-0)^{2} + (0-0)^{2}$ = $\sqrt a^{2}$ =a
BC = $\sqrt (a-a)^{2} + (b-0)^{2}$ = $\sqrt b^{2}$ = b
Therefore in triangle ABC
$AC^{2}$ = $AB^{2}$ + $BC^{2}$
$(\sqrt (a^{2}+b^{2})^{2}$ = $a^{2}$ + $b^{2}$
$a^{2}$ + $b^{2}$ = $a^{2}$ + $b^{2}$
Therefore it satisfy the Pythagoras theorem.
therefore triangle ABC is a right triangle
