Math Problem Statement

Assume points A, B, C are on the same line. If AB=8 and BC=3, then what is the length of AC?

Solution

If points AA, BB, and CC are collinear and in order along the same straight line, the length of ACAC is simply the sum of ABAB and BCBC, as the points form a single segment.

AC=AB+BCAC = AB + BC

Substitute the values:

AC=8+3=11AC = 8 + 3 = 11

Thus, the length of ACAC is 11\mathbf{11}.


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Related Questions:

  1. What if AB=8AB = 8 and BC=3BC = 3, but BB is between AA and CC?
  2. How would the calculation change if the points were not collinear?
  3. If AA, BB, and CC are coordinates in 3D space, how would you calculate ACAC?
  4. What is the significance of collinearity in geometry?
  5. How do you represent points and distances in a coordinate system?

Tip: Always verify the order of points when calculating distances to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Geometry
Line Segments
Collinearity

Formulas

Length of a line segment: AC = AB + BC

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 6-8