Problem

Which of the following slopes show that the set of points $C(1,-1), D(3,4), E(5,8)$ are not collinear? $2 / 5,1 / 2,4 / 9$ $5 / 2,2,9 / 4$ $-2,2,9 / 4$ $2,3,5 / 2$

Solution

Step 1 :Given the points C(1,-1), D(3,4), E(5,8), we need to determine if they are collinear. This can be done by calculating the slope between each pair of points and checking if they are equal.

Step 2 :The slope between two points (x1, y1) and (x2, y2) is given by \((y2 - y1) / (x2 - x1)\).

Step 3 :Calculating the slope between points C and D, we get \(slope_{CD} = (4 - (-1)) / (3 - 1) = 2.5\).

Step 4 :Calculating the slope between points D and E, we get \(slope_{DE} = (8 - 4) / (5 - 3) = 2.0\).

Step 5 :Calculating the slope between points C and E, we get \(slope_{CE} = (8 - (-1)) / (5 - 1) = 2.25\).

Step 6 :The slopes between the points are not equal, which means the points are not collinear. The slopes are 2.5, 2.0, and 2.25.

Step 7 :Final Answer: The slopes that show the points are not collinear are \(\boxed{2.5, 2.0, 2.25}\).

From Solvely APP
Source: https://solvelyapp.com/problems/15805/

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