Answer:
P(-7, 7.25)
Explanation:
Given the line segment RS, we want to find the coordinate of point P that divides RS in the ratio 1:3.
To do this, we usually apply the internal division of a line formula below:
[tex]P(x,y)=\mleft(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\mright)[/tex]
First, find the endpoints R and S from the graph.
[tex]\begin{gathered} (x_1,y_1)=R(-8,9) \\ (x_2,y_2)=S(-4,2) \\ \text{The ratio of division: }m\colon n=1\colon3 \end{gathered}[/tex]
Substitute the values into the formula:
[tex]\begin{gathered} P(x,y)=(\dfrac{1(-4)_{}+3(-8)}{1+3},\dfrac{1(2)+3(9)}{1+3}) \\ =(\dfrac{-4-24}{4},\dfrac{2+27}{4}) \\ =(\dfrac{-28}{4},\dfrac{29}{4}) \\ =(-7,7\dfrac{1}{4}) \\ \implies P(x,y)=\mleft(-7,7.25\mright) \end{gathered}[/tex]
The coordinate of point P that divides RS in the ratio 1:3 is (-7, 7.25).
