On a number line, point P corresponds to -3 and point Q corresponds to 5. If point R is th… — GRE General Test

On a number line, point $P$ corresponds to $-3$ and point $Q$ corresponds to $5$ . If point $R$ is the midpoint of line segment $PQ$ , what is the value of $|R - P|$ ?

A
$2$
$4$ Answer
C
$8$
D
$1$
E
$15$

Answer

The correct distance between point P and midpoint R is 4.

The total distance between

P (-3)

and

Q (5)

on the real number line is

|5 - (-3)| = 8

. Since

R

is the midpoint of segment

PQ

, it splits the total length into two equal halves of length

4

. Therefore, the distance from

P

R

, represented by

|R - P|

, is

4

Step-by-Step Solution

Calculate the total distance between points P and Q on the number line.

Distance

PQ = |5 - (-3)| = |5 + 3| = 8

The distance between any two points

a

and

b

on a number line is given by

|b - a|

Find the coordinate of the midpoint R.

Coordinate of

R = \frac{-3 + 5}{2} = \frac{2}{2} = 1

The midpoint coordinate is the average of the coordinates of the two endpoints.

Calculate the absolute distance between R and P.

|R - P| = |1 - (-3)| = |1 + 3| = 4

The absolute value gives the non-negative distance between the midpoint and point P.

Key Concept

Distance on a Number Line and Midpoint Formula

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Step-by-Step Solution

Key Concept

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