Question

Find the coordinates of the point $R$ which lies on the line $PQ$ produced such that $PR = 2QR$, where coordinates of points $P$ and $Q$ are $(7, -1)$ and $(-3, 4)$ respectively.

Accepted Answer

Since $R$ lies on $PQ$ produced and $PR = 2QR$, $Q$ is the midpoint of $PR$. Let $R = (x, y)$. By midpoint formula: $$-3 = \frac{7 + x}{2} \implies 7 + x = -6 \implies x = -13$$ $$4 = \frac{-1 + y}{2} \implies -1 + y = 8 \implies y = 9$$ Thus, coordinates of $R$ are $(-13, 9)$.

Coordinates of a point on extended line segment

Explanation

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