Question

of point c.

1. point d is 8 units from its opposite on a number line. write the numbers that point d and its opposite represent.

1. use the number line to complete parts (a) and (b).

a. plot point f at (-5).
b. plot point g at (-(-5)).
c. describe the relationship between point f and point g.

1. write the number and describe its relationship to 0 on a number line.

a. ten
b. the opposite of ten
c. the opposite of the opposite of ten

1. sasha says that (-(-25)) is equal to (-25). julie disagrees and says that (-(-25)) is equal to 25. who is correct? explain.

Explanation:

Question 6

Step1: Define opposite of a number

The opposite of a number \( x \) is \( -x \). Let point \( D \) represent the number \( x \), then its opposite is \( -x \).

Step2: Set up the distance equation

The distance between \( x \) and \( -x \) on a number line is \( |x - (-x)| = |2x| \). We know this distance is 8, so \( |2x| = 8 \).

Step3: Solve for \( x \)

Divide both sides by 2: \( |x| = 4 \). This gives \( x = 4 \) or \( x = -4 \).

Point \( F \) is at \( -5 \) and point \( G \) is at \( 5 \). On a number line, two numbers that are opposites are equidistant from 0 and lie on opposite sides of 0. The distance from \( F \) to 0 is \( |-5| = 5 \), and the distance from \( G \) to 0 is \( |5| = 5 \). So, \( F \) and \( G \) are opposites of each other (or additive inverses) and are equidistant from 0.

The number "Ten" is \( 10 \). On a number line, \( 10 \) is 10 units to the right of 0.

Answer:

Point \( D \) and its opposite represent \( 4 \) and \( -4 \) (or \( -4 \) and \( 4 \)).

Question 7

Part (a)

To plot point \( F \) at \( -5 \), find the position on the number line corresponding to \( -5 \) (5 units to the left of 0) and mark it as \( F \).

Part (b)

First, simplify \( -(-5) \). The opposite of \( -5 \) is \( 5 \), so \( -(-5)=5 \). Plot point \( G \) at \( 5 \) (5 units to the right of 0) on the number line.

Part (c)