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Sagot :
Given directed line segments from (-10,-5) to (5,1) with ratio 1:2
The coordinate for the partition on the line segment is given by the formula
[tex]\begin{gathered} (\frac{(mx_2+nx_1)_{}_{}}{m+n}),\text{ (}\frac{(my_2+ny_1)}{m+n} \\ \text{where m and n are the ratios} \end{gathered}[/tex]From the formula, let us define, all the parameters from the given coordinates and ratio
[tex]\begin{gathered} m=1;\text{ n=2} \\ x_{_1}=-10;x_2=5;y_1=-5;y_2=1;\text{ m=1; n=2} \end{gathered}[/tex]Substituting the parameters into the formula to the coordinate of the partition will give
[tex]\begin{gathered} =(\frac{(1\times5+2\times-10)}{1+2}),\text{ (}\frac{(1\times1+2\times-5)}{1+2}) \\ =(\frac{(5-20)}{3}),(\frac{(1-10)}{3}) \\ =(\frac{-15}{3},\frac{-9}{3}) \\ =(-5,-3) \end{gathered}[/tex]Hence, the coordinates of the point on the directed line segment that partitions the segment into the ratio 1 to 2 is (-5,-3)
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