Math Problem Statement

How do you calculate the distances between points B, C, and A on a number line?

Solution

To solve for BCBC and CACA, we'll calculate the distance between points BB and CC, as well as points CC and AA, on the number line. The formula to calculate the distance between two points is:

Distance=x2x1\text{Distance} = |x_2 - x_1|

Calculations:

  1. For BCBC: BC=CB=17.112.8=4.3BC = |C - B| = |17.1 - 12.8| = 4.3

  2. For CACA: CA=CA=17.1(9)=17.1+9=26.1CA = |C - A| = |17.1 - (-9)| = |17.1 + 9| = 26.1

Final Results:

  • BC=4.3BC = 4.3
  • CA=26.1CA = 26.1

Would you like a detailed explanation of each step?


Here are 5 related questions you might consider:

  1. How can we calculate distances on a coordinate plane instead of a number line?
  2. How does the concept of absolute value apply to distance calculations?
  3. What changes in distance calculations if a third dimension (z-axis) is introduced?
  4. How are midpoint and distance formulas related?
  5. Can distance formulas be used in real-world applications like navigation?

Tip: When solving problems on a number line, always visualize the direction and use the absolute value to ensure the distance is positive.

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Math Problem Analysis

Mathematical Concepts

Distance on a number line
Absolute value

Formulas

Distance formula: |x2 - x1|

Theorems

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Suitable Grade Level

Grades 6-8