Answer:
Hence, the coordinate of point M that divides the line segment AB is [tex](5, \frac{32}{3} )[/tex].
Step-by-step explanation:
Given that,
AB is the line segment, and M divides the line segment AB into a ratio of 2:1.
Coordinate of point A is [tex](-1, 2)[/tex] and Coordinate of point B is [tex](8, 15)[/tex].
Let, the coordinate of point M is [tex](x. y)[/tex].
Now,
The coordinate of a point M, 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 M is [tex]\frac{(2\times 8)+(1\times -1)}{(2+1)}[/tex] = [tex]\frac{(16-1)}{3} =\frac{15}{3} =5[/tex]
[tex]y[/tex] coordinate of point M is [tex]\frac{(2\times 15)+(1\times 2)}{(2+1)}[/tex] = [tex]\frac{30+2}{3} = \frac{32}{3}[/tex]
Hence, the coordinate of point M that divides the line segment AB is [tex](5, \frac{32}{3} )[/tex].
