On a standard number line, point R has coordinate -18 and point T has coordinate 22. Point… — ACT

On a standard number line, point $R$ has coordinate $-18$ and point $T$ has coordinate $22$ . Point $S$ lies on the line segment $RT$ such that the distance from $R$ to $S$ is $\frac{3}{5}$ of the distance from $R$ to $T$ . What is the coordinate of point $S$ ?

Answer: 6

Answer

The distance between

R(-18)

and

T(22)

is calculated using absolute value:

|22 - (-18)| = 40

. Taking

\frac{3}{5}

of 40 yields 24 units. Adding 24 to the starting coordinate

-18

gives the coordinate of point

S

as 6.

Step-by-Step Solution

Calculate the total distance between points

R

and

T

Distance

= |22 - (-18)| = |40| = 40

units

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

Determine the distance from

R

S

Distance

= \frac{3}{5} \times 40 = 24

units

Point

S

is located at a distance equal to

\frac{3}{5}

of the total segment length starting from

R

Calculate the coordinate of point

S

Coordinate of

S = -18 + 24 = 6

Since

S

lies between

R(-18)

and

T(22)

, moving from

R

toward

T

corresponds to increasing the coordinate value by 24.

Key Concept

Calculating distance between signed integers using absolute value and finding a point dividing a number line segment in a given ratio

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