The points A(-2,1), B(0,5) and C(-1,2) are collinear. check the statement is true or false.

Explanation

To determine whether the points A(-2, 1), B(0, 5), and C(-1, 2) are collinear, we need to check if the slopes of the line segments AB, BC, and AC are equal. If the slopes are equal, the points are collinear; if not, they are not collinear.

### Step-by-step Solution:

1. **Identify the coordinates of the points:**
- A = (-2, 1)
- B = (0, 5)
- C = (-1, 2)

2. **Calculate the slope of line segment AB:**
- The formula for the slope (m) between two points (x1, y1) and (x2, y2) is:
\[ m = \frac{y2 - y1}{x2 - x1} \]
- For points A and B:
- \(x1 = -2\), \(y1 = 1\)
- \(x2 = 0\), \(y2 = 5\)
- Substitute the values into the slope formula:
\[ m_{AB} = \frac{5 - 1}{0 - (-2)} = \frac{4}{2} = 2 \]

3. **Calculate the slope of line segment BC:**
- For points B and C:
- \(x1 = 0\), \(y1 = 5\)
- \(x2 = -1\), \(y2 = 2\)
- Substitute the values into the slope formula:
\[ m_{BC} = \frac{2 - 5}{-1 - 0} = \frac{-3}{-1} = 3 \]

4. **Calculate the slope of line segment AC:**
- For points A and C:
- \(x1 = -2\), \(y1 = 1\)
- \(x2 = -1\), \(y2 = 2\)
- Substitute the values into the slope formula:
\[ m_{AC} = \frac{2 - 1}{-1 - (-2)} = \frac{1}{1} = 1 \]

5. **Compare the slopes:**
- We found:
- \(m_{AB} = 2\)
- \(m_{BC} = 3\)
- \(m_{AC} = 1\)
- Since \(m_{AB} \neq m_{BC} \neq m_{AC}\), the slopes are not equal.

6. **Conclusion:**
- Since the slopes are not equal, the points A, B, and C are not collinear. Therefore, the statement that the points are collinear is **false**.