Question

Hi can you please help me with questions 5 on my home work

Answer 1

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:

`P(x,y)=\mleft((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\mright)`

First, find the endpoints R and S from the graph.

`\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}`

Substitute the values into the formula:

`\begin{gathered} P(x,y)=(\frac{1(-4)_{}+3(-8)}{1+3},(1(2)+3(9))/(1+3)) \\ =((-4-24)/(4),(2+27)/(4)) \\ =((-28)/(4),(29)/(4)) \\ =(-7,7(1)/(4)) \\ \implies P(x,y)=\mleft(-7,7.25\mright) \end{gathered}`

The coordinate of point P that divides RS in the ratio 1:3 is (-7, 7.25).