On a standard number line, the distance between two points, A and B, is 12 units. If the c… — ACT

On a standard number line, the distance between two points, $A$ and $B$ , is $12$ units. If the coordinate of point $A$ is $-18$ , which of the following is a possible coordinate for point $B$ ?

$-30$ Answer
B
$-12$
C
$-8$
D
$6$
E
$30$

Answer

-30

The correct answer is

-30

because the distance between two points on a number line is found by taking the absolute value of the difference between their coordinates. Setting up the relation

|b - (-18)| = 12

simplifies to

|b + 18| = 12

. Solving this absolute value equation yields two possible locations:

b + 18 = 12

(which gives

b = -6

) and

b + 18 = -12

(which gives

b = -30

). Among the choices,

-30

is the only possible coordinate listed.

Step-by-Step Solution

Set up the absolute value equation representing the distance between point A and point B on the number line.

Let

b

be the coordinate of point

B

. The distance between

A

and

B

is given by

|-18 - b| = 12

On a standard number line, the distance between any two coordinates

x

and

y

is given by the absolute value of their difference,

|x - y|

Solve the absolute value equation for the two possible cases.

Case 1:

-18 - b = 12 \Rightarrow -b = 30 \Rightarrow b = -30

. Case 2:

-18 - b = -12 \Rightarrow -b = 6 \Rightarrow b = -6

An equation of the form

|x| = d

(where

d \geq 0

) splits into two distinct equations:

x = d

and

x = -d

Compare the possible solutions with the given options.

The value

-30

is one of the possible coordinates and is listed in the options.

To identify which of the two mathematically correct coordinates (-30 or -6) is provided as an answer choice.

Key Concept

The distance between two points on a number line with coordinates

x

and

y

is represented by the absolute value of their difference,

|x - y|

Estimated Time:45s

Question

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Key Concept

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