Question

line ab has endpoints at -2 and 12, respectively.
a) use the number line to plot points a and b.
b) plot the the midpoint c of the segment.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Explanation:

Part (a)

To plot points \( A \) and \( B \) on the number line:

• Point \( A \) is at \( -2 \), so we locate \( -2 \) on the number line (between \( -3 \) and \( -1 \)) and mark it as \( A \).
• Point \( B \) is at \( 12 \), so we locate \( 12 \) on the number line (between \( 11 \) and \( 13 \)) and mark it as \( B \).

Part (b)

To find the midpoint \( C \) of segment \( AB \), we use the midpoint formula for two points \( x_1 \) and \( x_2 \) on a number line, which is \( \text{Midpoint} = \frac{x_1 + x_2}{2} \).

Step 1: Identify the endpoints

Here, \( x_1 = -2 \) (coordinate of \( A \)) and \( x_2 = 12 \) (coordinate of \( B \)).

Step 2: Apply the midpoint formula

Substitute the values into the formula:
\[
\text{Midpoint} = \frac{-2 + 12}{2}
\]

Step 3: Simplify the expression

First, calculate the numerator: \( -2 + 12 = 10 \).
Then, divide by 2: \( \frac{10}{2} = 5 \).

So, the midpoint \( C \) is at \( 5 \). We locate \( 5 \) on the number line (between \( 4 \) and \( 6 \)) and mark it as \( C \).

For part (a), plot \( A \) at \( -2 \) and \( B \) at \( 12 \) on the given number line. For part (b), the midpoint \( C \) is at \( \boldsymbol{5} \), so plot \( C \) at \( 5 \) on the number line.

Answer:

Part (a)

To plot points \( A \) and \( B \) on the number line:

• Point \( A \) is at \( -2 \), so we locate \( -2 \) on the number line (between \( -3 \) and \( -1 \)) and mark it as \( A \).
• Point \( B \) is at \( 12 \), so we locate \( 12 \) on the number line (between \( 11 \) and \( 13 \)) and mark it as \( B \).

Part (b)

To find the midpoint \( C \) of segment \( AB \), we use the midpoint formula for two points \( x_1 \) and \( x_2 \) on a number line, which is \( \text{Midpoint} = \frac{x_1 + x_2}{2} \).

Step 1: Identify the endpoints

Here, \( x_1 = -2 \) (coordinate of \( A \)) and \( x_2 = 12 \) (coordinate of \( B \)).

Step 2: Apply the midpoint formula

Substitute the values into the formula:
\[
\text{Midpoint} = \frac{-2 + 12}{2}
\]

Step 3: Simplify the expression

First, calculate the numerator: \( -2 + 12 = 10 \).
Then, divide by 2: \( \frac{10}{2} = 5 \).

So, the midpoint \( C \) is at \( 5 \). We locate \( 5 \) on the number line (between \( 4 \) and \( 6 \)) and mark it as \( C \).

For part (a), plot \( A \) at \( -2 \) and \( B \) at \( 12 \) on the given number line. For part (b), the midpoint \( C \) is at \( \boldsymbol{5} \), so plot \( C \) at \( 5 \) on the number line.