Answered

IDNLearn.com is the place where your questions are met with thoughtful and precise answers. Find in-depth and accurate answers to all your questions from our knowledgeable and dedicated community members.

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.

Sagot :

GinnyAnsweridn
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.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.