Question

show that the points 0, 3 and 0, 1 and 2, 3 are the vertex of equilateral triangle​

Answer 1

Answer:

Step-by-step explanation:

Hope helpful

Mark as brainlist answer

Tnx

Answer 2

Answer:  The triangle is isosceles, not equilateral.

Step-by-step explanation:  Let the given points be A(0, 3), B(0, 1) and C(2, 3).

We are to show that ΔABC is equilateral, i.e., AB = BC = CA.

The length of a side will be given by the distance between the two corresponding vertices.

For example, the distance between two points (a, b) and (c, d) is given by

$D=\sqrt{(c-a)^2+(d-b)^2}.$

We have,

$AB=\sqrt{(0-0)^2+(1-3)^2}=\sqrt{0+4}=\sqrt{4}=2,\\\\BC=\sqrt{(2-0)^2+(3-1)^2}=\sqrt{4+4}=\sqrt 8=2\sqrt 2,\\\\CA=\sqrt{(0-2)^2+(3-3)^2}=\sqrt{4+0}=\sqrt 4=2.$

Since AB = CA ≠ BC, so the vertices A, B, C are of an isosceles triangle, not an equilateral triangle.

The isosceles triangle ABC is shown in the attached figure.