To solve the problem, let’s calculate the number of triangles and quadrilaterals that can be formed from the given points.

Key details:

• 8 points: 4 are collinear, and 4 are non-collinear.
• No three points are collinear except the 4 collinear points.

---

Step 1: Total number of triangles

The total number of ways to choose 3 points from 8 points is:

$\binom{8}{3} = \frac{8 \cdot 7 \cdot 6}{3 \cdot 2 \cdot 1} = 56$

However, triangles cannot be formed using collinear points. There is exactly one subset of 3 collinear points from the 4 collinear points:

$\binom{4}{3} = 4$

Thus, the number of triangles that can be formed is:

$\text{Valid triangles} = 56 - 4 = 52$

---

Step 2: Total number of quadrilaterals

The total number of ways to choose 4 points from 8 points is:

$\binom{8}{4} = \frac{8 \cdot 7 \cdot 6 \cdot 5}{4 \cdot 3 \cdot 2 \cdot 1} = 70$

Quadrilaterals cannot be formed using all 4 collinear points. There is exactly one subset of 4 collinear points:

$\binom{4}{4} = 1$

Thus, the number of quadrilaterals that can be formed is:

$\text{Valid quadrilaterals} = 70 - 1 = 69$

---

Step 3: Calculate $a + b$ and $a - b$

Here, $a = 52$ (triangles), and $b = 69$ (quadrilaterals).

1. $a + b = 52 + 69 = 121$
2. $a - b = 69 - 52 = 17$

---

Answer:

None of the provided options match the calculations. If you'd like, I can re-evaluate the assumptions or interpretations of the problem. Would you like to discuss this further or clarify any constraints?

Follow-Up Questions:

1. Would you like a detailed breakdown of the triangle and quadrilateral calculations?
2. Are there any additional constraints or clarifications to the problem?
3. Should we consider more specific configurations of points or arrangements?
4. Would you like to understand how collinearity affects combinatorics further?
5. Do you want me to verify the subtraction aspect in detail?

Tip:

Always double-check how special cases (like collinear points) affect your calculations in geometry-based combinatorics.