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

7 or 31

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

7 and 31

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.