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Points [tex]$A$[/tex], [tex]$B$[/tex], and [tex]$C$[/tex] are collinear, and [tex]$B$[/tex] is between [tex]$A$[/tex] and [tex]$C$[/tex]. Given [tex]$AB = 12$[/tex] and [tex]$AC = 19$[/tex], what is [tex]$BC$[/tex]?

Sagot :

GinnyAnsweridn
Let's solve the problem step-by-step:

1. Understand the given information:
- Points [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] are collinear, meaning they lie on a straight line.
- Point [tex]\(B\)[/tex] is between points [tex]\(A\)[/tex] and [tex]\(C\)[/tex].
- The distance [tex]\(AB\)[/tex] is 12 units.
- The distance [tex]\(AC\)[/tex] is 19 units.

2. Recall the geometric relationship on a straight line:
- Since [tex]\(B\)[/tex] is between [tex]\(A\)[/tex] and [tex]\(C\)[/tex], the distance from [tex]\(A\)[/tex] to [tex]\(C\)[/tex] ([tex]\(AC\)[/tex]) can be thought of as the sum of distances [tex]\(AB\)[/tex] and [tex]\(BC\)[/tex].

3. Set up the equation using the given distances:
[tex]\[ AC = AB + BC \][/tex]

4. Substitute the given values into the equation:
- [tex]\(AC = 19\)[/tex]
- [tex]\(AB = 12\)[/tex]

[tex]\[ 19 = 12 + BC \][/tex]

5. Solve the equation for [tex]\(BC\)[/tex]:
[tex]\[ BC = 19 - 12 \][/tex]

6. Perform the subtraction:
[tex]\[ BC = 7 \][/tex]

So, the distance [tex]\(BC\)[/tex] is [tex]\(7\)[/tex] units.
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