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:

$PQ=\frac{4}{7}PR$

This way,

$(x,y)-(-18,17)=\frac{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:

$(-6,1)$