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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.

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Let's solve this problem step-by-step:

1. Understand the Points and the Ratio:
- Point F is at 4.
- Point G is at -2.
- The ratio of the segments FH to HG is given as 3:9. This ratio simplifies to 1:3.

2. Calculate the Total Distance:
- The distance between F and G (total distance) is the difference between F and G's positions on the number line.
- Distance = F - G
- Distance = 4 - (-2) = 4 + 2 = 6.

3. Divide the Distance According to the Ratio:
- The ratio 1:3 means that if the total distance is divided into 4 equal parts (since 1+3=4), FH will correspond to 1 part and HG will correspond to 3 parts.
- Each part of the distance is 6 / 4 = 1.5.

4. Calculate the Length of FH:
- Since FH is one part, FH = 1.5.

5. Determine the Position of Point H:
- Point H is between F and G, and FH is 1.5. Starting from F (which is at 4), we move 1.5 units towards G (in the negative direction).
- Position of H = F - FH = 4 - 1.5 = 2.5.

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