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: Define total segment length

Let the length of $\overline{MN} = 7$ units.

Step2: Find length of $\overline{MP}$

Since $P$ is $\frac{4}{7}$ of the distance from $M$ to $N$,
$\overline{MP} = \frac{4}{7} \times 7 = 4$ units

Step3: Find length of $\overline{PN}$

Subtract $\overline{MP}$ from total length:
$\overline{PN} = 7 - 4 = 3$ units

Step4: Determine the ratio

The ratio $\overline{MP}:\overline{PN} = 4:3$

Answer:

B. 4:3