A(-1, 1), C(1, 4) and B(7, 13) are plotted on a graph sheet.
Use the section formula to test whether C lies on the segment AB and, if it does, give AC : CB.

Assume AC : CB = $m:n$. From $x:1=\frac{7m-n}{m+n}$, so $m+n=7m-n$ and $2n=6m$, giving $m:n=1$ : 3. Now test that ratio on $y:\frac{1\cdot 13+3\cdot 1}{4}=\frac{16}{4}=4$, which is exactly C's $y$-coordinate, so C does lie on AB and AC : CB = 1 : 3. Choosing 'C does not lie on AB' means the $y$-check was never carried out; 3 : 1 reverses $m$ and $n$; 1 : 4 quotes AC : AB instead of AC : CB.