The co-ordinates of A, B, C are respectively (-4, 0), (0, 2) and (-3, 2). Check whether points are collinear.

Answer

To determine whether the points A, B, and C are collinear, we can use the concept of slope. The points are collinear if the slope of the line segment joining any two pairs of points is the same.

### Step-by-Step Solution:

1. **Identify the coordinates of the points:**
- A = (-4, 0)
- B = (0, 2)
- C = (-3, 2)

2. **Calculate the slope of line segment AB:**
- The formula for the slope (M) between two points (x1, y1) and (x2, y2) is:
\[ M = \frac{y_2 - y_1}{x_2 - x_1} \]
- For points A and B:
- \(x_1 = -4, y_1 = 0\)
- \(x_2 = 0, y_2 = 2\)
- Substitute the values into the slope formula:
\[ M_{AB} = \frac{2 - 0}{0 - (-4)} = \frac{2}{4} = \frac{1}{2} \]

3. **Calculate the slope of line segment BC:**
- For points B and C:
- \(x_1 = 0, y_1 = 2\)
- \(x_2 = -3, y_2 = 2\)
- Substitute the values into the slope formula:
\[ M_{BC} = \frac{2 - 2}{-3 - 0} = \frac{0}{-3} = 0 \]

4. **Compare the slopes:**
- We found:
- \(M_{AB} = \frac{1}{2}\)
- \(M_{BC} = 0\)
- Since \(M_{AB} \neq M_{BC}\), the slopes are not equal.

5. **Conclusion:**
- Since the slopes of line segments AB and BC are not equal, the points A, B, and C are **not collinear**.