are these collinear??

Question

1. (11, 3), (9, -1), and (17, 15)
2. (-11, -8), (-6, 10), and (26, -12)
3. (-1, -12), (-6, 19), and (-10, 15)
4. (-17, -12), (5, -10), and (-6, -11)
5. (16, 14), (3, 4), and (42, 34)
6. (-6, -2), (-15, 4), and (-12, 2)
7. (-10, 9), (-14, 9), and (-25, 0)
8. (-6, 2), (16, 12), and (37, 35)
9. (12, -19), (3, 13), and (48, -147)
10. (-11, 3), (-16, 13), and (-1, -17)

Answer 1

1).
Gradient of first two points = (-1-3)/(9-11) = 2
gradient of last two points = (15+1/(17-9) = 2
They have the same slope and a common point, hence they are colinear.

Answer 2

Suppose you have 3 distinct points P1 = (a1, b1), P2 = (a2, b2) and P3 = (a3, b3). To see if they are collinear, you have to verify if the line joining P1 and P2 has the same slope of the line joining P2and P3. So, you have to check if (b2 - b1)/(a2 - a1) = (b3 - b2)/(a3 - a2), if no denominator is null. If a2 = a1 you have a vertical line, and the 3 points will be collinear if and only if a2 = a3.

Now, just check.