Question

Suppose A,R, and B are collinear on AB and AR: AB=1/4, what are the coordinates of R?

Answer 1

Since AR:AB=1/4, then AR:RB=1/3, therefore, using the following formula for the coordinates of the point R

`x=(x_1+rx_2)/(1+r),\text{ y=}(y_1+y_2r)/(1+r),`

we get:

`\begin{gathered} x=(1+(1)/(3)\cdot4)/(1+(1)/(3))=(1+(4)/(3))/(1+(1)/(3))=((7)/(3))/((4)/(3))=(7)/(4), \\ y=(-1+(1)/(3)\cdot4)/(1+(1)/(3))=(-1+(4)/(3))/(1+(1)/(3))=((1)/(3))/((4)/(3))=(1)/(4). \end{gathered}`

Answer:

`R=((7)/(4),(1)/(4))=(1.75,0.25)\text{.}`