Discussion
Find the value of 'a' for which the points (a, 1), (1, -1), and (11, 4) are collinear.
Answer: B
Correct answer: 5
The two fully known points fix the line. Its slope is
\[m = \frac{4 - (-1)}{11 - 1} = \frac{5}{10} = \frac{1}{2}\]
For (a, 1) to lie on the same line, the slope from it to (1, -1) must also be \(\tfrac{1}{2}\):
\[\frac{-1 - 1}{1 - a} = \frac{1}{2} \quad\Longrightarrow\quad \frac{-2}{1-a} = \frac{1}{2} \quad\Longrightarrow\quad -4 = 1 - a \quad\Longrightarrow\quad a = 5\]
Checking with the third point: the slope from (5, 1) to (11, 4) is \(\tfrac{3}{6} = \tfrac{1}{2}\), as required.
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