What are the coordinates of point C below segment AC that is partitioned at point B in a ratio of 2 to 5.

The coordinates of points C are:[tex]x=\frac{31}{2} \ and \y=0 \\ \\ \\ C(\frac{31}{2},0)[/tex]Explanation:The figure related to this problem has been attached below. Here we have two points:[tex]A(x_{1},x_{2})=A(5,0) \\ \\ B(x_{1},x_{2})=B(8,0)[/tex]So we need to find the point C:[tex]C(x,y)[/tex]So we need to use the formula for externally division of a line segment as follows:[tex](x_{2},y_{2})=( \frac {mx + nx_{1}}{m + n},\frac {my + ny_{1}}{m + n}  )[/tex][tex]Where: \\ \\ m:n=2:5[/tex]So:[tex](8,0)=( \frac {2x + 5(5)}{2 + 5},\frac {2y + 5(0)}{2 + 5}  ) \\ \\ \bullet \ \frac{2x+25}{7}=8 \\ \\ 2x+25=56 \\ \\ 2x=32 \\ \\ x=\frac{31}{2} \\ \\ \\  \bullet \ \frac{2y}{7}=0 \\ \\ y=0[/tex]So the coordinates of points C are:[tex]x=\frac{31}{2} \ and \y=0 \\ \\ \\ C(\frac{31}{2},0)[/tex]Learn more:Partition of segments: