Question

what are the coordinates of the point on the directed line segment from (-10,-5) to (5,1) that partitions the segment into a ratio of 1 to 2

Answer 1

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

`\begin{gathered} (\frac{(mx_2+nx_1)_{}_{}}{m+n}),\text{ (}((my_2+ny_1))/(m+n) \\ \text{where m and n are the ratios} \end{gathered}`

From the formula, let us define, all the parameters from the given coordinates and ratio

`\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}`

Substituting the parameters into the formula to the coordinate of the partition will give

`\begin{gathered} =(((1*5+2*-10))/(1+2)),\text{ (}((1*1+2*-5))/(1+2)) \\ =(((5-20))/(3)),(((1-10))/(3)) \\ =((-15)/(3),(-9)/(3)) \\ =(-5,-3) \end{gathered}`

Hence, the coordinates of the point on the directed line segment that partitions the segment into the ratio 1 to 2 is (-5,-3)