Question

Show that points A(1, 2) , B(1, 5), C(4, 2) are the vertices of a right-angled triangle.

Answer 1

Answer:

Step-by-step explanation:

AB=$\sqrt{(1-1)^{2} +(5-2)^{2} }$   = 3

BC=$\sqrt{(4-1)^{2} +(2-5)^{2} }$  = 3$\sqrt{2}$

CA=$\sqrt{(1-4)^{2} +(2-2)^{2} }$  =3

HERE AC IS THE LONGEST SIDE OF THE TRINGLE

⇒$AB^{2} +AC^{2}$ =3²+3²=18 =(3√2)²=BC²

∴The given points  are the vertices of a right angle tringle.