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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.



Answer :

GinnyAnswer
To solve for the location of point H between points F and G on a number line, follow these steps:

1. Identify the coordinates of points F and G:
- [tex]\( F \)[/tex] is at 4
- [tex]\( G \)[/tex] is at -2

2. Understand the ratio of segments [tex]\( FH \)[/tex] to [tex]\( HG \)[/tex]:
- The ratio given is [tex]\( FH:HG = 3:9 \)[/tex]
- This ratio simplifies to [tex]\( 1:3 \)[/tex]

3. Calculate the total ratio and the total distance between F and G:
- Total ratio (adding the parts of the ratio): [tex]\( 1 + 3 = 4 \)[/tex]
- Total distance between F and G ([tex]\( FG \)[/tex]): [tex]\( 4 - (-2) = 6 \)[/tex] units

4. Break the total distance into parts according to the ratio:
- Since the ratio is [tex]\( 1:3 \)[/tex], the distance [tex]\( FG \)[/tex] (6 units) is divided into 4 parts.
- Each part = [tex]\( 6 \div 4 = 1.5 \)[/tex] units

5. Calculate the distances for [tex]\( FH \)[/tex] and [tex]\( HG \)[/tex]:
- [tex]\( FH = 1.5 \)[/tex] parts [tex]\( \times 1 \text{ (the part for FH)} = 1.5 \)[/tex] units
- [tex]\( HG = 1.5 \)[/tex] parts [tex]\( \times 3 \text{ (the parts for HG)} = 4.5 \)[/tex] units

6. Determine the exact location of point H:
- Point H is [tex]\( 1.5 \)[/tex] units away from point F (since [tex]\( FH = 1.5 \)[/tex] units)
- Starting from F (which is at 4), moving [tex]\( 1.5 \)[/tex] units towards G (left on the number line):
[tex]\( 4 - 1.5 = 2.5 \)[/tex]

Therefore, point H is at [tex]\( 2.5 \)[/tex] on the number line.

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