If the points A(k, 2k), B(3k, 3k), and C(3, 1) are collinear, what is the value of k?
Answer and explanation
Correct answer: C. k = -1/3
- Step 1: Slope AB = (3k - 2k) / (3k - k) = k / 2k = 1/2.
- Step 2: Slope BC = (1 - 3k) / (3 - 3k).
- Step 3: Equating slopes: 1/2 = (1 - 3k) / (3 - 3k) => 3 - 3k = 2(1 - 3k) = 2 - 6k.
- Step 4: -3k + 6k = 2 - 3 => 3k = -1 => k = -1/3.
Why not the others: k = 1/3, k = -1 and k = 2/3 do not fit.
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