Answer:
Yes, two sides are perpendicular and the side lengths fit the Pythagoras theorem.
Step-by-step explanation:
Given the triangle whose coordinates are A(0,2), B(-2, -1) and C(1, -3)
we have to find the given triangle is right angled triangle or not.
First we have to find the length of sides of triangle ABC
[tex]\text{By distance formula, the length of line joining the points }(x_1,y_1)\text{ and }(x_2, y_2)[/tex]
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, length of AB, BC, and AC is
[tex]AB=\sqrt{(-2-0)^2+(-1-2)^2}=\sqrt{4+9}=\sqrt{13} units[/tex]
[tex]BC=\sqrt{(1-(-2))^2+(-3-(-1))^2}=\sqrt{9+4}=\sqrt{13} units[/tex]
[tex]AC=\sqrt{(1-0)^2+(-3-2)^2}=\sqrt{1+25}=\sqrt{26} units[/tex]
If given triangle is right angled triangle then the length of sides must satisfy Pythagoras theorem i.e
[tex]AC^2=AB^2+BC^2[/tex]
[tex](\sqrt{26})^2=(\sqrt{13})^2+(\sqrt{13})^2[/tex]
[tex]26=13+13[/tex]
[tex]26=26[/tex]
which is true.
Hence, Pythagoras theorem is satisfied.
Hence option C is correct.
