f. Are (58,20),(48,16) and (5,8) collinear?

To determine if the points $(58,20)$, $(48,16)$, and $(5,8)$ are collinear, we can use the concept of slope.<br /><br />The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:<br /><br />$$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$<br /><br />Let's calculate the slopes of the lines passing through the pairs of points:<br /><br />1. Slope of the line passing through $(58,20)$ and $(48,16)$:<br />$$\text{slope} = \frac{16 - 20}{48 - 58} = \frac{-4}{-10} = \frac{2}{5}$$<br /><br />2. Slope of the line passing through $(58,20)$ and $(5,8)$:<br />$$\text{slope} = \frac{8 - 20}{5 - 58} = \frac{-12}{-53} = \frac{12}{53}$$<br /><br />3. Slope of the line passing through $(48,16)$ and $(5,8)$:<br />$$\text{slope} = \frac{8 - 16}{5 - 48} = \frac{-8}{-43} = \frac{8}{43}$$<br /><br />Since the slopes of the lines passing through the pairs of points are not equal, the points $(58,20)$, $(48,16)$, and $(5,8)$ are not collinear.