Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar
on a number line, point d is at -3, and point e is at 6. the point f lies on de. the ratio of df to fe is 2:3. where does point f lie on the number line?
point f is at on the number line.

Explanation:

Step1: Calculate the distance between D and E

The distance between \(D(-3)\) and \(E(6)\) is \(6 - (-3)=9\).

Step2: Divide the distance according to the ratio

Since the ratio \(DF:FE = 2:3\), the total number of parts is \(2 + 3=5\). Each part has a length of \(\frac{9}{5}=1.8\).

Step3: Find the coordinate of F

The length of \(DF\) is \(2\times1.8 = 3.6\). Starting from \(D(-3)\) and moving \(3.6\) units towards \(E\), the coordinate of \(F\) is \(-3+3.6 = 0.6=\frac{3}{5}\).

Answer:

\(\frac{3}{5}\)