Question

You have a line AB where A is (0,3) and B is (2,7) find a point P that partitions the line 1:2.

Answer 1

`P=((2)/(3),(13)/(3))`

Explanation:

We have the following formula to calculate the point P

`\begin{gathered} x_p=(x_2\cdot a+x_1\cdot b)/(a+b)_{} \\ y_p=(y_2\cdot a+y_1\cdot b)/(a+b)_{} \\ a\colon b=1\colon2 \\ (x_1,y_1)=(0,3) \\ (x_2,y_2)=(2,7) \end{gathered}`

Replacing:

`\begin{gathered} x_p=(2\cdot1+0\cdot2)/(1+2)=(2+0)/(3)=(2)/(3) \\ y_p=(7\cdot1+3\cdot2)/(1+2)=(7+6)/(3)=(13)/(3) \\ \text{The point p is:} \\ ((2)/(3),(13)/(3)) \end{gathered}`