Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
No
To check whether the three points are collinear, we find the slopes of any two pairs of points.
First, consider the points \((1, 5)\) and \((2, 3)\). The slope is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
Substituting values: \( m_{12} = \frac{3 - 5}{2 - 1} = \frac{-2}{1} = -2 \).
Next, consider the points \((2, 3)\) and \((-2, -11)\). Using the slope formula again:
\( m_{23} = \frac{-11 - 3}{-2 - 2} = \frac{-14}{-4} = \frac{7}{2} \).
Since \( m_{12} = -2 \) and \( m_{23} = \frac{7}{2} \) are not equal, the slopes between the points are different.
If the points were collinear, all slopes would be equal. Because they differ, the points are not collinear.