Answer:
Hence, the coordinate of point P is [tex](\frac{40}{7}, \frac{66}{7})[/tex].
Step-by-step explanation:
Given that,
AB is the line segment having endpoints are A and B.
Coordinate of point A is [tex](4, 8)[/tex] and coordinate of point B is [tex](10, 13)[/tex].
Point P lies on line segment AB which divides the line segment AB in the 2:5.
Let, the coordinate of point P which divides the line segment AB is [tex](x, y)[/tex].
Now,
The coordinate of a point P, which divides the line segment AB internally in the ratio [tex]m_{1} :m_{2}[/tex] are given by:
[tex]\frac{m_{1}x_{2}+m_{2}x_{1} }{m_{1}+m_{2} } , \frac{m_{1}y_{2}+m_{2}y_{1} }{m_{1}+m_{2} }[/tex]
[tex]x[/tex] coordinate of point P is [tex]\frac{2\times 10+5\times 4}{2+5} =\frac{20+20}{7}=\frac{40}{7}[/tex]
[tex]y[/tex] coordinate of point P is [tex]\frac{2\times 13+5\times 8}{2+5} =\frac{26+40}{7} =\frac{66}{7}[/tex]
Hence, the coordinate of point P is [tex](\frac{40}{7}, \frac{66}{7})[/tex].
