To determine if the points (3, 6), (2, 9), and (0, 4) are collinear, we need to check if the slopes between each pair of points are equal.
1. **Find the slope between the first two points (3, 6) and (2, 9):**
The formula for slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 – y1) / (x2 – x1)
Plugging in the coordinates of the points:
m1 = (9 – 6) / (2 – 3) = 3 / -1 = -3
2. **Now, find the slope between the second and third points (2, 9) and (0, 4):**
Using the same slope formula:
m2 = (4 – 9) / (0 – 2) = -5 / -2 = 5/2
3. **Finally, find the slope between the first and third points (3, 6) and (0, 4):**
m3 = (4 – 6) / (0 – 3) = -2 / -3 = 2/3
Since the slopes m1, m2, and m3 are not equal (-3, 5/2, and 2/3 respectively), we can conclude that the points (3, 6), (2, 9), and (0, 4) are not collinear.
Final Answer: False