Line RS passes through points R (5, 3) and S (-1, 0).
Line PQ is parallel to line RS and passes through points P (3, -1) and Q (-2, y).
What are the coordinates of point Q ?
$$\small{\text{Line PQ is parallel to line RS - cross product }}
\boxed{|(\vec{S}-\vec{R}) \times (\vec{Q}-\vec{P})| = 0}\\ \\
\left|
\left[
\binom{-1}{0}-\binom{5}{3}
\right]
\times
\left[
\binom{-2}{y}-\binom{3}{-1}
\right]
\right| = 0\\\\
\left|
\binom{-6}{-3} \times \binom{-5}{y+1}
\right| = 0\\\\
(-6)\cdot(y+1)-(-3)\cdot(-5) = 0\\
(-6)\cdot(y+1)-15 = 0\\
(-6)\cdot(y+1)=15\\\\
y+1=-\frac{15}{6}\\\\
y=-\frac{15}{6}-1\\\\
y=-\frac{21}{6}\\\\
y= -\frac{7}{2}\\\\
y=-3.5\\\\
\boxed{\vec{Q}=\binom{-2}{-3.5}}$$

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