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.

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

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=\frac{2}{2+3}(8-3)+3=\frac{2}{5}(5)+3=2+3=5 \\ x=\frac{2}{2+3}(1-(-9))-9=\frac{2}{5}(1+9)-9=\frac{2}{5}\cdot10-9=4-9=-5 \end{gathered}$

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