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 f is at 4, and point g is at -2. point h lies between point f and point g. if the ratio of fh to hg is 3 : 9, where does point h lie on the number line?

point h is at on the number line.

Explanation:

Identify the coordinates and ratio

Given points on a number line:

$$ F = 4,\quad G = -2 $$

Point \(H\) lies between \(F\) and \(G\). The ratio of the lengths is:

$$ FH : HG = 3 : 9 = 1 : 3 $$

Set up the partition equation

Let \(h\) be the coordinate of point \(H\). Since \(H\) is between \(F(4)\) and \(G(-2)\):

$$
LATEXBLOCK0
$$

Using the ratio \(FH : HG = 1 : 3\):

$$ \frac{4 - h}{h + 2} = \frac{1}{3} $$

Solve for the coordinate

$$
LATEXBLOCK1
$$

Answer:

Point H is at <blank>\(2.5\)</blank> on the number line.