The points $$\left(0, \frac{8}{3}\right)$$, $$(1, 3)$$ and $$(82, 30)$$

To determine the nature of the points $$\left(0, \frac{8}{3}\right)$$, $$(1, 3)$$, and $$(82, 30)$$, we first check if they are collinear, meaning they lie on a straight line. Three points are collinear if the area of the triangle they form is zero. The area formula for a triangle with vertices $$(x_1, y_1)$$, $$(x_2, y_2)$$, and $$(x_3, y_3)$$ is:

$$\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$$

Substituting the given points:

$$x_1 = 0$$, $$y_1 = \frac{8}{3}$$

$$x_2 = 1$$, $$y_2 = 3$$

$$x_3 = 82$$, $$y_3 = 30$$

Compute the differences:

$$y_2 - y_3 = 3 - 30 = -27$$

$$y_3 - y_1 = 30 - \frac{8}{3} = \frac{90}{3} - \frac{8}{3} = \frac{82}{3}$$

$$y_1 - y_2 = \frac{8}{3} - 3 = \frac{8}{3} - \frac{9}{3} = -\frac{1}{3}$$

Now plug into the area formula:

$$\text{Area} = \frac{1}{2} \left| 0 \cdot (-27) + 1 \cdot \left(\frac{82}{3}\right) + 82 \cdot \left(-\frac{1}{3}\right) \right|$$

Simplify inside the absolute value:

$$0 + \frac{82}{3} - \frac{82}{3} = 0$$

So,

$$\text{Area} = \frac{1}{2} \left| 0 \right| = 0$$

Since the area is zero, the points are collinear and lie on a straight line.

Alternatively, we can verify by checking the slopes between each pair of points. The slope between two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Slope between $$\left(0, \frac{8}{3}\right)$$ and $$(1, 3)$$:

$$m_1 = \frac{3 - \frac{8}{3}}{1 - 0} = \frac{\frac{9}{3} - \frac{8}{3}}{1} = \frac{\frac{1}{3}}{1} = \frac{1}{3}$$

Slope between $$(1, 3)$$ and $$(82, 30)$$:

$$m_2 = \frac{30 - 3}{82 - 1} = \frac{27}{81} = \frac{1}{3}$$

Slope between $$\left(0, \frac{8}{3}\right)$$ and $$(82, 30)$$:

$$m_3 = \frac{30 - \frac{8}{3}}{82 - 0} = \frac{\frac{90}{3} - \frac{8}{3}}{82} = \frac{\frac{82}{3}}{82} = \frac{82}{3} \times \frac{1}{82} = \frac{1}{3}$$

All slopes are equal to $$\frac{1}{3}$$, confirming that the points are collinear.

Since the points lie on a straight line, they do not form a triangle. Therefore, options A, B, and D, which describe types of triangles, are incorrect.

Hence, the correct answer is Option C.