Question

If point P is 4/7 of the distance from M to N, then point P partitions the directed line segment from M to N into a __?__ ratio. 4:1 4:3 4:7 4:11

Answer 1

Let

x-------> the distance MN

we know that

$MP=\frac{4}{7}x \\\\PN=\frac{3}{7}x$

Find the ratio $MP:PN$

$ratio=\frac{MP}{PN} \\ \\ratio= \frac{(4/7)x}{(3/7)x} \\ \\ratio= \frac{4}{3}$

therefore

the answer is

$4:3$

Answer 2

Answer:

Point P partitions the directed line segment from M to N into a 4 : 11 ratio.

Step-by-step explanation:

Since, point P is 4/7 of the distance from M to N,

$\implies \frac{MP}{MN}=\frac{4}{7}$

Let MP = 4x and MN = 7x,

Where x is any number,

⇒ PN = MP + MN = 4x + 7x = 11x,

Thus, the ratio at which P divides the line segment from M to N is,

$\frac{MP}{PN}=\frac{4x}{11x}=\frac{4}{11}$

Hence, point P partitions the directed line segment from M to N into a 4 : 11 ratio.