Question

The point Q lies on the segment PR. Find the coordinates of Q so that PQ is 4/7 of PR.

Answer 1

Segment PQ is described by the vector:

`\begin{gathered} (3,-11)-(-18,17) \\ \rightarrow(21,-28) \end{gathered}`

Let point q be:

`(x,y)`

We know that:

`PQ=(4)/(7)PR`

This way,

`(x,y)-(-18,17)=(4)/(7)(21,-28)`
`\begin{gathered} (x+18,y-17)=(12,-16) \\ \Rightarrow x+18=12\rightarrow x=-6 \\ \Rightarrow y-17=-16\rightarrow y=1 \end{gathered}`

This way, point q is:

`(-6,1)`