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
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?
Step 1: Understanding the Ratio
The ratio of FH to HG is given as 3:9. This means that for every 3 units of FH, there are 9 units of HG. We can simplify this ratio by dividing both numbers by their greatest common divisor, which is 3.
Step 2: Simplifying the Ratio
Simplifying the ratio, we get FH:HG = 1:3. This means that for every 1 unit of FH, there are 3 units of HG.
Step 3: Finding the Distance Between F and G
The distance between F and G is the absolute value of the difference between their coordinates. In this case, the distance between F and G is |4 - (-2)| = 6 units.
Step 4: Finding the Position of H
Since the ratio of FH to HG is 1:3, we can divide the distance between F and G into 4 parts, with 1 part being FH and 3 parts being HG. To find the position of H, we need to find the point that divides the distance between F and G in a 1:3 ratio.
Step 5: Calculating the Position of H
Let's calculate the position of H. Since the distance between F and G is 6 units, we can divide it into 4 parts, with 1 part being FH and 3 parts being HG. The position of H will be 1/4 of the distance between F and G from F.
Step 6: Finding the Coordinate of H
To find the coordinate of H, we need to add 1/4 of the distance between F and G to the coordinate of F. The coordinate of F is 4, and the distance between F and G is 6 units. So, 1/4 of the distance between F and G is 6/4 = 1.5 units.
Step 7: Calculating the Coordinate of H
The coordinate of H will be the coordinate of F plus 1.5 units. So, the coordinate of H is 4 + 1.5 = 5.5.
Q: What is the significance of the ratio of FH to HG in this problem?
A: The ratio of FH to HG is 3:9, which means that for every 3 units of FH, there are 9 units of HG. This ratio is crucial in determining the position of point H on the number line.
Q: How do I simplify the ratio of FH to HG?
A: To simplify the ratio, we divide both numbers by their greatest common divisor, which is 3. This simplifies the ratio to 1:3, meaning that for every 1 unit of FH, there are 3 units of HG.
Q: What is the distance between points F and G on the number line?
A: The distance between points F and G is the absolute value of the difference between their coordinates. In this case, the distance between F and G is |4 - (-2)| = 6 units.
Q: How do I find the position of point H on the number line?
A: To find the position of point H, we need to divide the distance between F and G into 4 parts, with 1 part being FH and 3 parts being HG. We then add 1/4 of the distance between F and G to the coordinate of F to find the coordinate of H.
Q: What is the coordinate of point H on the number line?
A: The coordinate of point H is 4 + 1.5 = 5.5.
Q: Why is it important to use the correct ratio of FH to HG in this problem?
A: Using the correct ratio of FH to HG is crucial in determining the position of point H on the number line. If the ratio is incorrect, the position of point H will also be incorrect.
Q: Can I use a different ratio of FH to HG in this problem?
A: No, the ratio of FH to HG is given as 3:9, and we must use this ratio to find the position of point H. Using a different ratio will result in an incorrect position for point H.
Q: How do I apply this concept to real-world problems?
A: This concept can be applied to real-world problems involving ratios and proportions. For example, in architecture, the ratio of the height of a building to its width may be critical in determining the stability of the structure.
Q: What are some common mistakes to avoid when working with ratios and proportions?
A: Some common mistakes to avoid when working with ratios and proportions include:
- Using the wrong ratio or proportion
- Not simplifying the ratio or proportion
- Not considering the context of the problem
- Not checking the units of measurement
Q: How can I practice working with ratios and proportions?
A: You can practice working with ratios and proportions by:
- Solving problems involving ratios and proportions
- Creating your own problems involving ratios and proportions
- Using online resources and practice exercises
- Working with a tutor or mentor