Question

Show that points (2,0),(-2,0),(0,2) are the vertices of triangle also state with reason type of triangle ​

Answer 1

Answer:

Right triangle.

Step-by-step explanation:

Since, a triangle is possible if  the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let, A≡(2,0), B≡(-2,0) and C≡(0,2),

Since,  by the distance formula,

$AB=\sqrt{(-2-2)^2+(0-0)^2}$

$=\sqrt{-4^2+0^2}$

$=\sqrt{4^2}=4\text{ unit}$

$BC=\sqrt{(0+2)^2+(2-0)^2}$

$=\sqrt{2^2+2^2}$

$=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\text{ unit}$

$CA=\sqrt{(2-0)^2+(0-2)^2}$

$=\sqrt{2^2+-2^2}$

$=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\text{ unit}$

Since, AB < BC + CA,

Hence, the triangle ABC is possible,

Also, AB² = BC² + CA²

⇒ ∠ABC = 90° ( By Pythagoras theorem )

Thus,  triangle ABC is a right angled triangle.

Answer 2

Answer:

triangle ABC is the right angle triangle

Step-by-step explanation:

the one side square is equal sum of square of other two side