k = 4
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Check if the slope between any two points is the same as the slope between the other two points.
The slope between (7, -2) and (5, 1) is given by:
- m₁ = (1 - (-2))/(5 - 7) = 3/(-2) = -3/2
The slope between (5, 1) and (3, k) is given by:
- m₂ = (k - 1)/(3 - 5) = (k - 1)/(-2)
For the points to be collinear, m₁ must be equal to m₂.
Setting the two slopes equal to each other and solving for 'k', we have:
Solving for 'k', we get:
- k - 1 = (2)(3/2)
- k - 1 = 3
- k = 4