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: https://brainly.com/question/14096093
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