Position-Ratio of Point/Examples

Examples of Position-Ratios of Points

Let $P$ and $Q$ be points.

Let $R$ be a point on the straight line passing through $P$ and $Q$.

Let $k$ denote the position-ratio of $R$.

$R$ Approaching $P$

As $R$ approaches $P$, $k \to 0$.

$R$ Approaching $Q$

As $R$ approaches $Q$ where $R$ is on the line segment $PQ$, $k \to +\infty$.

As $R$ approaches $Q$ where $R$ is not on the line segment $PQ$, $k \to -\infty$.

$R$ Approaching Infinity

As $R$ approaches the point at infinity on the left, $k \to -1$ from above.

As $R$ approaches the point at infinity on the right, $k \to -1$ from below.

$R$ Midway between $P$ and $Q$

When $R$ is on the midpoint of the line segment $PQ$, $k = +1$.

This is the centroid of $P$ and $Q$.