Question

use the diagram below to place each of the described points on the numbered line.
r -45 q -11 p 7 n 34 m 49
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
\\(\frac{1}{3}\\) of the distance from p to n
\\(\frac{3}{4}\\) of the distance from r to p

Explanation:

For \(\boldsymbol{\frac{1}{3}}\) of the distance from \(P\) to \(N\):

Step1: Find distance from \(P\) to \(N\)

\(P = 7\), \(N = 34\), distance \(= 34 - 7 = 27\)

Step2: Calculate \(\frac{1}{3}\) of the distance

\(\frac{1}{3} \times 27 = 9\)

Step3: Find the point

Start at \(P(7)\), move \(9\) units: \(7 + 9 = 16\)

For \(\boldsymbol{\frac{3}{4}}\) of the distance from \(R\) to \(P\):

Step1: Find distance from \(R\) to \(P\)

\(R = -45\), \(P = 7\), distance \(= 7 - (-45) = 52\)

Step2: Calculate \(\frac{3}{4}\) of the distance

\(\frac{3}{4} \times 52 = 39\)

Step3: Find the point

Start at \(R(-45)\), move \(39\) units: \(-45 + 39 = -6\)

Answer:

\(\frac{1}{3}\) of the distance from \(P\) to \(N\) is at \(16\); \(\frac{3}{4}\) of the distance from \(R\) to \(P\) is at \(-6\)