Math Buddyv1.0

Segment addition calculator

Enter the segment lengths. MathBuddy uses AB + BC = AC to find x or the missing length.

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What this page covers

  • The additive property of length: when BB lies on segment ACAC, AB+BC=ACAB + BC = AC.
  • Finding xx when the lengths are written as expressions, then any length you ask for.
  • Midpoint problems, where the two halves of a segment are equal.
  • Not covered here: lengths from coordinates (use the geometry calculator), and segments that do not lie on one line.

How to enter the problem

  • Type it or paste it. Say which point lies between the others, then give each length, for example AB = 2x + 3, BC = 4x - 1, AC = 26.
  • Scan it. Fit the one problem in the frame.
  • Choose a photo. Several problems in one photo are solved as a list.
  • Then tap Solve.

Worked examples

Example 1

Problem

Point B\displaystyle B lies between A\displaystyle A and C\displaystyle C. AB=9\displaystyle AB = 9 and BC=14\displaystyle BC = 14. Find AC\displaystyle AC.

Answer

Verified

The answer is

AC=23AC = 23

Explanation

  1. Write the segment addition rule
    AC=AB+BCAC = AB + BC
  2. Add the parts
    AC=9+14=23AC = 9 + 14 = 23

Example 2

Problem

Point B\displaystyle B lies between A\displaystyle A and C\displaystyle C. AB=3x\displaystyle AB = 3x, BC=2x+5\displaystyle BC = 2x + 5 and AC=40\displaystyle AC = 40. Find BC\displaystyle BC.

Answer

Verified

The answer is

BC=19BC = 19

Explanation

  1. Write the equation
    3x+(2x+5)=403x + (2x + 5) = 40
  2. Solve for xx
    5x+5=405x + 5 = 40, so 5x=355x = 35 and x=7x = 7.
  3. Find the length asked for
    BC=2(7)+5=19BC = 2(7) + 5 = 19
  4. Check the total
    AB=21AB = 21, and 21+19=4021 + 19 = 40.

Example 3

Problem

M\displaystyle M is the midpoint of PQ\displaystyle PQ. PM=3x+1\displaystyle PM = 3x + 1 and MQ=5x−7\displaystyle MQ = 5x - 7. Find PQ\displaystyle PQ.

Answer

Verified

The answer is

PQ=26PQ = 26

Explanation

  1. Use the midpoint
    A midpoint splits the segment into two equal parts, so 3x+1=5x−73x + 1 = 5x - 7.
  2. Solve for xx
    8=2x8 = 2x, so x=4x = 4.
  3. Find each half
    PM=3(4)+1=13PM = 3(4) + 1 = 13 and MQ=5(4)−7=13MQ = 5(4) - 7 = 13.
  4. Add the halves
    PQ=13+13=26PQ = 13 + 13 = 26

Common mistakes

  • Stopping at xx when a length is asked for. In the second example x=7x = 7, but BC=19BC = 19.
  • Setting the two parts equal when BB is not a midpoint. Parts are equal only at a midpoint.
  • Giving only one half for a midpoint question. PQPQ is twice PMPM: 2626, not 1313.

Checks, assumptions and limits

  • Check by hand: put xx back into every length and confirm the parts add up to the whole.
  • Every length must come out positive. A value of xx that makes a length zero or negative means the setup is wrong.
  • MathBuddy can make mistakes. Double check important steps.

Related tasks

Frequently asked questions

If a point B lies on the segment from A to C, the two shorter pieces add up to the whole: AB + BC = AC.

Yes. Say which length you want. The steps solve for x first, then put it back in to find that length.

Yes. Say that the point is a midpoint. The two halves are set equal, and the whole is twice one half.

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Last updated: · MathBuddy