Question

if point p is \\( \frac { 4 } { 7 } \\) of the distance from m to n, what ratio does the point p partition the directed line segment from m to n into?
4:1
4:3
4:7
4:10

Explanation:

Step1: Analyze the given fraction

If point \(P\) is \(\frac{4}{7}\) of the distance from \(M\) to \(N\), then the distance from \(M\) to \(P\) is \(4\) parts and the distance from \(P\) to \(N\) is \(7 - 4=3\) parts.

Step2: Determine the ratio

The ratio of \(MP\) to \(PN\) (the partition ratio) is \(4:3\) as the ratio of the two - segment lengths formed by the point \(P\) on the line segment \(MN\).

Answer:

B. \(4:3\)