Question

I need Geometry help

Answer 1

We have the points A(-2, 5) and B(12, 0).

And we must find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 4 to 1.

To find the coordinates we must use the next equations

Where (x1, y1) and (x2, y2) are the given points and a:b is the given ratio.

- x-coordinate

`\begin{gathered} -2+(4)/(4+1)(12-(-2)) \\ =-2+(56)/(5) \\ =(46)/(5) \end{gathered}`

- y-coordinate

`\begin{gathered} 5+(4)/(4+1)(0-5) \\ =5+(-20)/(5) \\ =1 \end{gathered}`

Finally, the point P is

`P((46)/(5),1)`