Answer :
Lines can be divided in smaller segments by using ratios
The coordinates of B are: [tex]\mathbf{ (\frac{4}{3},-\frac{10}{3})}[/tex]
The given parameters are:
[tex]\mathbf{A =(-2,5)}[/tex]
[tex]\mathbf{C =(2,-5)}[/tex]
[tex]\mathbf{m : n = 5 : 1}[/tex]
The coordinate of B is calculated using:
[tex]\mathbf{B = \frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n}}[/tex]
So, we have:
[tex]\mathbf{B = \frac{5 \times 2 + 1 \times -2}{5 +1},\frac{5 \times -5 + 1 \times 5}{5 + 1}}[/tex]
[tex]\mathbf{B = (\frac{8}{6},\frac{-20}{6})}[/tex]
Simplify fraction
[tex]\mathbf{B = (\frac{4}{3},-\frac{10}{3})}[/tex]
Hence, the coordinates of B are: [tex]\mathbf{ (\frac{4}{3},-\frac{10}{3})}[/tex]
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