Question

Is the following shape a right triangle? how do you know? ​

Answer 1

I would go with c. It looks like point b is where the right triangle is

Answer 2

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

$\text{By distance formula, the length of line joining the points }(x_1,y_1)\text{ and }(x_2, y_2)$

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Therefore, length of AB, BC, and AC is

$AB=\sqrt{(-2-0)^2+(-1-2)^2}=\sqrt{4+9}=\sqrt{13} units$

$BC=\sqrt{(1-(-2))^2+(-3-(-1))^2}=\sqrt{9+4}=\sqrt{13} units$

$AC=\sqrt{(1-0)^2+(-3-2)^2}=\sqrt{1+25}=\sqrt{26} units$

If given triangle is right angled triangle then the length of sides must satisfy Pythagoras theorem i.e

$AC^2=AB^2+BC^2$

$(\sqrt{26})^2=(\sqrt{13})^2+(\sqrt{13})^2$

$26=13+13$

$26=26$

which is true.

Hence, Pythagoras theorem is satisfied.

Hence option C is correct.