Answer:
[tex]\left(\displaystyle -\frac{2}{5},\frac{4}{5}\right)[/tex]
Step-by-step explanation:
Proportions
The coordinates of the point R are (-6,4) and the coordinates of the point S are (8,-4). We must find the coordinates of a point P(x,y) such that the ratio of segment RP to segment PS is 2/3. Let's find the coordinates separately. In the x-axis:
[tex]\displaystyle \frac{-6-x}{x-8}=\frac{2}{3}[/tex]
Operating and rearranging
[tex]-18-3x=2x-16[/tex]
Solving
[tex]\displaystyle x=-\frac{2}{5}[/tex]
Now for the y-axis
[tex]\displaystyle \frac{4-y}{y+4}=\frac{2}{3}[/tex]
Operating and rearranging
12-3y=2y+8
Solving
[tex]\displaystyle y=\frac{4}{5}[/tex]
Thus, the point that partitions the segment in the ratio 2 to 3 is
[tex]\left(\displaystyle -\frac{2}{5},\frac{4}{5}\right)[/tex]
