If the points A(2, 3), B(5, k) and C(6, 7) are collinear then ______.

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If the points A(2, 3), B(5, k) and C(6, 7) are collinear then k = 6. Explanation: For collinearity slopes AB and AC must be equal. Slope AB = (k - 3)/(5 - 2) = (k - 3)/3 Slope AC = (7 - 3)/(6 - 2) = $\frac{4}{4}$ = 1 Set (k - 3)/3 = 1 $\Rightarrow$ k – 3 = 3 $\Rightarrow$ k = 6

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