The segment joining A(-2, -3) and B(6, 5) meets the $x$-axis at a point C.
Find the coordinates of C.

On the $x$-axis $y=0$, so $\frac{5m-3n}{m+n}=0$, giving $5m=3n$ and $m:n=3$ : 5. Then $x=\frac{3\cdot 6+5\cdot (-2)}{8}=\frac{18-10}{8}=1$, so $C$ = (1, 0). (3, 0) uses the inverted ratio 5 : 3; (2, 0) takes the midpoint's $x$-coordinate instead of solving for the crossing; (0, 1) writes the correct number in the wrong slot — a point on the $x$-axis has the form $(x$, 0), not (0, $x$).