The coordinate of the point q are x=5 and y=9 that is Q(5,9).
We have given that RQ : QS = 3 : 1 .
points R(5,-3),S(5,13)
What are the points coordinate of vector RQ and QS?
Let point Q has coordinates (x,y). Consider vectors [tex]\overrightarrow{RQ}[/tex] and [tex]\overrightarrow{QS}[/tex]. Note that
[tex]\overrightarrow{RQ}=(x-5,y+3);[/tex]
[tex]\overrightarrow{QS}=(5-x,13-y).[/tex]
So we have given that,
[tex]Since \dfrac{RQ}{QS}=\dfrac{3}{1}, then[/tex]
[tex]\dfrac{\overrightarrow{RQ}}{\overrightarrow{QS}}=\dfrac{3}{1},[/tex]
Thus,
[tex]\dfrac{x-5}{5-x}=\dfrac{3}{1}\Rightarrow x-5=3(5-x),\ x-5=15-3x,\ 4x=20,\ x=5.\\ \\\dfrac{y+3}{13-y}=\dfrac{3}{1}\Rightarrow y+3=3(13-y),\ y+3=39-3y,\ 4y=36,\ y=9.[/tex]
Therefore we get the coordinate of the point q are x=5 and y=9.
That is Q(5,9).
To learn more about the coordinate of vector visit:
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