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?\
\\(\bigcirc\\) 4:1\
\\(\bigcirc\\) 4:3\
\\(\bigcirc\\) 4:7\
\\(\bigcirc\\) 4:10

Explanation:

Step1: Understand the distance ratio

Point \( P \) is \( \frac{4}{7} \) of the distance from \( M \) to \( N \). So the distance from \( M \) to \( P \) is \( \frac{4}{7}MN \), and the distance from \( P \) to \( N \) is \( MN - \frac{4}{7}MN=\frac{3}{7}MN \).

Step2: Find the ratio \( MP:PN \)

The ratio of \( MP \) to \( PN \) is \( \frac{4}{7}MN:\frac{3}{7}MN \). The \( MN \) and \( \frac{1}{7} \) cancel out, giving \( 4:3 \).

Answer:

B. 4:3