Since AR:AB=1/4, then AR:RB=1/3, therefore, using the following formula for the coordinates of the point R
[tex]x=\frac{x_1+rx_2}{1+r},\text{ y=}\frac{y_1+y_2r}{1+r},[/tex]
we get:
[tex]\begin{gathered} x=\frac{1+\frac{1}{3}\cdot4}{1+\frac{1}{3}}=\frac{1+\frac{4}{3}}{1+\frac{1}{3}}=\frac{\frac{7}{3}}{\frac{4}{3}}=\frac{7}{4}, \\ y=\frac{-1+\frac{1}{3}\cdot4}{1+\frac{1}{3}}=\frac{-1+\frac{4}{3}}{1+\frac{1}{3}}=\frac{\frac{1}{3}}{\frac{4}{3}}=\frac{1}{4}. \end{gathered}[/tex]
Answer:
[tex]R=(\frac{7}{4},\frac{1}{4})=(1.75,0.25)\text{.}[/tex]
