Answer:
We have a line that passes through points C and D.
a) Points C and D determine one unique line
This is true, there is only one line that passes through a given pair of points, then we can call this line as "Line CD".
b) There are infinitely many points between points C and D.
This is also true, if we define the points with real numbers in R^2, we will have a dense set, which means that between C and D we can find infinite points.
c) The distance from C to D is equal to the distance from D to C.
Also true, the distance between two points C = (cx, cy) and D = (dx, dy) is defined as:
D = √( (cx - dx)^2 + (cy - dy)^2)
And because we have squares, this will be exactly the same as:
D = √( (dx - cx)^2 + (dy - cy)^2)
Then the distance from C to D, is exactly the same as the distanco from D to C.
d) Any line segment that contains point C must also contain point D.
This is false, we can define infinite segments where the endpoint is C, and does not pass through point D (some examples are given in the image below) So this is the only false option.
