Question

which expression represents the distance between P(2) and Q (-2)
A.|-2 + 2|
B.|2- -2
C. 2 + -2
D.|2| - |-2|

Answer 1

To find the distance between the points \( P(2) \) and \( Q(-2) \) on the number line, you can use the formula for distance between two points:

\[
\text{Distance} = |x_1 - x_2|
\]

Here, \( x_1 = 2 \) and \( x_2 = -2 \). Thus, the distance is:

\[
|2 - (-2)| = |2 + 2| = |4| = 4
\]

Now, let's evaluate the options:

A. \(|-2 + 2| = |0| = 0\)

B. \( |2 - -2| = |2 + 2| = |4| = 4\)

C. \( 2 + -2 = 0\)

D. \(|2| - |-2| = 2 - 2 = 0\)

The correct expression that represents the distance between \( P(2) \) and \( Q(-2) \) is **B**: \( |2 - -2| \) or \( |2 + 2| \).