Question

Point N lies on segment MP . The distance between points M and P is 24 cm. The distance between points N and M is twice the distance between N and P. Find NP and NM.

Answer 1

Let the distance between points N and P be denoted as \( x \) cm. Since the distance between points N and M is twice the distance between N and P, we can express the distance between N and M as \( 2x \) cm.

According to the given information, the total distance between M and P can be represented as the sum of the distances from M to N and from N to P. Therefore, we can set up the following equation:

\[
NM + NP = MP
\]
Substituting the known values into the equation, we have:

\[
2x + x = 24
\]

Combining like terms results in:

\[
3x = 24
\]

Now, we can solve for \( x \):

\[
x = \frac{24}{3} = 8 \text{ cm}
\]

Now that we have the distance \( NP \) (which is \( x \)), we can find \( NM \):

\[
NM = 2x = 2 \times 8 = 16 \text{ cm}
\]

Therefore, the distances are:
- \( NP = 8 \) cm
- \( NM = 16 \) cm