Question

Show that points (2,0),(-2,0)and (0,2) are the vertices of of a triangle. Also state with reason the type of the triangle.

Answer 1

it is a isosceles triangle

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Answer 2

Answer:

Isosceles triangle.

Step-by-step explanation:

Let, A≡(2,0), B≡(-2,0) and C≡(0,2),

Since, by the distance formula,

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

$=\sqrt{(-4)^2+0^2$

$=\sqrt{16}=4$

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

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

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

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

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

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

Since,

BC = CA,

And, we know that if two sides of a triangle are equal then it is an isosceles triangle,

⇒ Triangle ABC is an isosceles triangle.