If the points `A(3,4),B(x_1 ,y _1) and C(x_2 ,y_2)` are such that both `3 , x_1, x_2 and 4, y_1 ,y_2` are in AP, then
`(i)` A , B , C are vertices of an isosceles triangle
`(ii)` A , B , C are collinear points
`(iii)` A , B , C are vertices of a right angle triangle
`(iv)` A , B , C are vertices of a scalene triangle
`(v)` A , B , C are vertices of a equilateral triangle

Explanation

To solve the problem, we need to analyze the conditions given for the points A, B, and C. The points are defined as follows:

- A(3, 4)
- B(x₁, y₁)
- C(x₂, y₂)

We know that the coordinates of these points must satisfy the condition that both sets of coordinates (3, x₁, x₂) and (4, y₁, y₂) are in Arithmetic Progression (AP).

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