Question

4. Line segment RW has endpoints R(-4,5) and W(6, 20). Point P is on RW such that RP.PW is 2:3. What are thecoordinates of point P?

Answer 1

The coordinates would be P(-3.2, 6.2)

We need to calculate the slope of the segment

`\begin{gathered} m=(20-5)/(6+4) \\ m=(15)/(10) \\ m=1.5 \end{gathered}`

The ratio 2:3 splits the segment into 5 sections. We will add 2/5 of the rise to the y-coordinate and 2/5 of the run to the x-coordinate:

`\begin{gathered} -4+\mleft(2/5\mright)\mleft(2\mright)=-4+4/5=-4+0.8=-3.2 \\ 5+\mleft(2/5\mright)\mleft(3\mright)=5+6/5=5+1.2=6.2 \end{gathered}`