Question

Given the endpoints (-9,3) and (1,8), partition the segment into the ratio 2:3.

Answer 1

To find the partition, we have to use the following formulas.

`\begin{gathered} y=(a)/(a+b)(y_2-y_1)+y_1 \\ x=(a)/(a+b)(x_2-x_1)+x_1 \end{gathered}`

Where a = 2 and b = 3. Let's replace the following coordinates.

`\begin{gathered} x_1=-9 \\ x_2=1 \\ y_1=3 \\ y_2=8 \end{gathered}`
`\begin{gathered} y=(2)/(2+3)(8-3)+3=(2)/(5)(5)+3=2+3=5 \\ x=(2)/(2+3)(1-(-9))-9=(2)/(5)(1+9)-9=(2)/(5)\cdot10-9=4-9=-5 \end{gathered}`

Hence, the point that divides the segment in a ratio 2:3 is (-5,5).