Question

Which of the following statements are true? Select all that apply.

The number line form minus six to six by increment of one and every tick mark is labeled. The point minus two is labeled as A. The point one is labeled as B. And the point six is labeled as C.
A. The length of AB¯¯¯¯¯¯ is –3.
B. d(B, C) = BC = |6 – 1|
C. AB + AC = BC
D. AB + BC = AC

Answer 1

B. d(B, C) = BC = |6 – 1|

D. AB + BC = AC

Explanation:

Given that:

On a number line :

Point A = - 2

Point B = 1

Point C = 6

Distance BC = d(B, C) = |6 - 1| = 5

Distance AB = |-2 - 1| = 3

AB + AC ;

AB = 3 ; AC= |-2 - 6| = 8 ; BC = |1 - 6| = 5

3 + 8 = 11

HENCE

AB + AC ≠ BC

AB + BC = AC

AC = |- 2 - 6| = 8

AB = 3 ; BC = |1 - 6| = 5

3 + 5 = 8

Hence,

AB + BC = AC