On a temperature monitor scale represented as a horizontal number line, sensor A is positi… — ACT

On a temperature monitor scale represented as a horizontal number line, sensor $A$ is positioned at coordinate $-18$ and sensor $B$ is positioned at coordinate $14$ . A relay station $C$ is located on the line segment between sensor $A$ and sensor $B$ such that the distance from sensor $A$ to relay station $C$ is $\frac{3}{4}$ of the total distance between sensor $A$ and sensor $B$ . What is the absolute value of the coordinate of relay station $C$ ?

Answer: 6

Answer

The absolute value of the coordinate of relay station

C

6

To find the distance between

A

(

-18

) and

B

(

14

), subtract

-18

from

14

to get

32

units. Three-fourths of

32

24

units. Adding

24

units to the starting coordinate

-18

yields

6

as the coordinate for

C

. The absolute value of

6

6

Step-by-Step Solution

Calculate the total distance between coordinates

-18

and

14

Distance =

|14 - (-18)| = |14 + 18| = 32

units

The distance between two points on a number line is given by the absolute value of the difference of their coordinates.

Calculate the distance from sensor

A

to relay station

C

Distance

AC = \frac{3}{4} \times 32 = 24

units

Relay station

C

is positioned

\frac{3}{4}

of the total distance away from

A

towards

B

Find the coordinate of relay station

C

Coordinate of

C = -18 + 24 = 6

Moving rightward from

-18

24

units gives the location of

C

Evaluate the absolute value of the coordinate of

C

|6| = 6

The problem asks for the absolute value of the coordinate of

C

Key Concept

Distance on a number line and absolute value evaluation

Estimated Time:1m 15s

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