Question

find the length of (overline{gh}).
number line image: d at -4, e at (-1\frac{1}{3}), f near e, g at 2, h at (3\frac{1}{2})
(gh = square)
(simplify your answer. type an integer, fraction, or mixed number.)

Explanation:

Step1: Identify coordinates of G and H

G is at \( 2 \), H is at \( 3\frac{1}{2} \) (which is \( \frac{7}{2} \) or \( 3.5 \)).

Step2: Calculate the distance

The length of a segment on a number line between two points \( a \) and \( b \) is \( |b - a| \). So, \( GH = |3\frac{1}{2}-2| \).
Convert \( 3\frac{1}{2} \) to improper fraction: \( 3\frac{1}{2}=\frac{7}{2} \), \( 2=\frac{4}{2} \).
Subtract: \( \frac{7}{2}-\frac{4}{2}=\frac{3}{2}=1\frac{1}{2} \).

Answer:

\( 1\frac{1}{2} \) (or \( \frac{3}{2} \))