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.

Answer 1

[AI-generated answer — Bot GPT-4o]

To find the location of point H on the number line, we need to use the given ratio between the segments FH and HG.

The ratio FH to HG is given as 3:9, which can be simplified to 1:3. This means HG is three times as long as FH.

First, let's determine the total distance between points F and G:
- Point F is at 4.
- Point G is at -2.

The distance between F and G is:
4 - (-2) = 4 + 2 = 6 units.

Since FH is 1 part and HG is 3 parts (totaling 4 parts):
- FH = 1 part
- HG = 3 parts

The total distance (6 units) is divided into 4 equal parts:
1 part = 6 / 4 = 1.5 units.

Since FH is 1 part:
- FH = 1.5 units

Point H is 1.5 units away from F towards G:

Point F is at 4:
- Point H = 4 - 1.5 = 2.5

Therefore, point H is at 2.5 on the number line.

So, point H is at **2.5** on the number line.