Question

Points A, B, and C are collinear. You are given AB=12 and AC=19. What is the possible value of BC?

Answer 1

Answer:

  7 or 31

Step-by-step explanation:

If the points are arranged BAC, the distance BC is BA+AC = 12 +19 = 31.

If the points are arranged ABC, the distance BC is AC-AB = 19 -12 = 7.

Answer 2

Answer:

7 and 31

Step-by-step explanation:

Given: Points A, B, and C are collinear. $AB=12$ and $AC=19$

To find: Possible value of BC.

Solution: There are two possible cases

Case 1: When B is between A and C.

Now, A, B, and C are collinear.

$AB+BC=AC$

$12+BC=19$

$BC=19-12$

$BC=7$

Case 2: When A is between C and B.

Now, C, A, and B are collinear.

$CA+AB=BC$

$19+12=BC$

$BC=31$

Hence, the possible values of BC are 7 and 31.