Three points either lie on one straight line or they do not. Drag them and watch the two short distances against the long one. When the two shorter lengths add up to exactly the longest, the middle point has nowhere left to be except on the line.
Drag A, B or CWatch AB + BC against ACThe shaded triangle vanishes when they line up
Points snap to whole numbers, so an exact match is reachable.
The three points
A
(-3, -4)
B
(0, 0)
C
(6, 8)
B is the point being tested. Drag it off the line and the test below fails immediately.
The distance test
AB
5.00
BC
10.00
AB + BC
15.00
AC
15.00
The sum matches AC exactly, so the three points are in a straight line.
Verdict
These three points are
in a straight line
Area of triangle ABC
0.00
Three points that line up cannot enclose any area. That is the same test written a second way, and it is the one that scales to harder problems.
Noescio