Find the value of 'a' for which the points (a, 1), (1, -1), and (11, 4) are collinear.
Answer: B
For the points to be collinear, the slope between any two pairs of points must be the same.
Let's find the slope between (1, -1) and (11, 4):
m = \(\frac{4 - (-1)}{11 - 1} = \frac{5}{10} = \frac{1}{2}\).
Now, the slope between (a, 1) and (1, -1) must also be 1/2.
\(\frac{-1 - 1}{1 - a} = \frac{1}{2} \Rightarrow \frac{-2}{1 - a} = \frac{1}{2}\)
Cross-multiply: -4 = 1 - a
a = 1 + 4 = 5. My calculation is 5. Let me re-check. -4=1-a => a=5. Let's check the answer key. B=-5. Let's see how. Did I make a mistake? -2/(1-a)=1/2. -4=1-a. a=5. Let's try slope between (a,1) and (11,4). (4-1)/(11-a) = 3/(11-a) = 1/2. 6=11-a. a=5. I am consistently getting 5. The answer key must be wrong. I will correct the answer option.