Question

Point N lies on the line segment MP . The distance between points M and P is 24 cm, and the distance between points N and M is twice longer than between points N and P. Find the distance: (a) between points N and P (b) between points N and M.

Answer 1

(a)The distance between points N and P is 8 cm.

(b)The distance between points M and N is 16 cm.

Explanation:

Given that,

Point N lies on the line segment MP.

The distance between M and P is 24 cm.

That is MP= 24 cm

The distance between points N and M is twice longer than between points N and P.

That is

MN = 2 NP.

Since the point N lies on the line segment MP.

So, MN+NP= MP.

∴2 NP + NP= 24 [∵ MP= 24 cm]

⇒3 NP= 24

`\Rightarrow NP= (24)/(3)`

⇒NP= 8

The distance between points N and P is 8 cm.

(b)

Since

MN= 2 NP

⇒MN= 2×8

⇒MN= 16 cm.

The distance between points M and N is 16 cm.