Answer
Triangle ABC is isosceles because two of the sides have side length equal to $\sqrt{34}$.
Work Step by Step
Step 1. Plot the coordinates
Step 2. Calculate the distances using the distance formula: $$Distance = \sqrt{(x_{2}−x_{1}){2}+(x_{2}−x_{1}){2}}$$
For line AB: $$\sqrt{((0−2)^{2}+(−2−6)^{2})}$$ $$=\sqrt {((−2)^{2}+(−8)^{2})}$$ $$=\sqrt{(4+64)}$$ $$=\sqrt{68}$$
For line BC: $$\sqrt{((5−0)^{2}+(1−(-2))^{2})}$$ $$=\sqrt {((5)^{2}+(3)^{2})}$$ $$=\sqrt{(25+9)}$$ $$\sqrt{34}$$
For line AC: $$\sqrt{((5−2)^{2}+(1−6))^{2})}$$ $$=\sqrt{((3)^{2}+(-5)^{2})}$$ $$=\sqrt{(9+25)}$$ $$=\sqrt{34}$$
Step 3: Draw your conclusion
Triangle ABC is isosceles because two of the sides have side length equal to $\sqrt{34}$.
