If r and s are positive numbers, what are the coordinates of the midp

Without going rephrasing the question, we can directly look at the statements. The only thing we see is that we need some kind of information about the two points M and N.

Looking at the statements we see that neither statements contains information about both points, so if we can get enough information to answer the question, it can only be from both statements combined. With that we can conclude:

To analyse the statements, lets make a the convention that the coordinates of M are larger. If that should not be the case, the result should differ by a minus.

The coordinates of the mid point of the line are the smaller coordinate plus half the difference between the larger and the smaller. Therefore, the x-coordinate is:

\(x=r-\frac{r-(3-r)}{2}\frac{2r-(r-(3-r))}{2}=\frac{2r-2r+3}{s}=\frac{3}{2}\)

and the y-coordinate is:

\(3-s-\frac{(3-s)-s}{2}=\frac{6+2s-3-2s}{2}=\frac{3}{2}\)

As both coordinates are independent of r and s, we know that answer C is correct.