Question

Are the set of points C(1, -1), D(3, 4), E(5, 8) are collinear?

Answer 1

No - the slope of a line through `(1, -1)` and `(3, 4)` is `5/2` while the slope of a line through `(3, 4)` and `(5, 8)` is `2`, so there is no one straight line that passes through all three.

Explanation:

If a line passes through `(x_1, y_1)` and `(x_2, y_2)` then its slope m is given by the formula:

`m = (Delta y) / (Delta x) = (y_2 - y_1) / (x_2 - x_1)`

So a line through `(1, -1)` and `(3, 4)` has slope:

`(4 - (-1))/(3-1) = 5/2`

and a line through `(3, 4)` and `(5, 8)` has slope:

`(8-4)/(5-3) = 4/2 = 2`