Question

The numbers given are the coordinates of the endpoints of a segment on a number line. Find the coordinate of the midpoint by taking the average.

a. 12, 34

b.$-3,7$

c.$17,-9$

d.$-5,-7$

Short answer

a. The coordinate of the midpoint is 23.

b. The coordinate of the midpoint is 2.

c. The coordinate of the midpoint is 4.

d. The coordinate of the midpoint is $-6$.

Step-by-step solution

a. Step 1- Apply the concept of the average of numbers.

The average of two numbers is calculated by adding up all the numbers, then dividing the total by the count of numbers.

Step 2- Find the sum of the numbers.

Here the numbers are 12 and 34.

Calculate the sum of the numbers as follows:

$\begin{array}{c}\text{Sumofthenumbers}=12+34\\ =46\end{array}$

Count of the numbers =2

Step 3- Find the average.

Divide the sum of the numbers to the count of the numbers to find the average of the numbers as follows:

$\begin{array}{c}\text{Average}=\frac{46}{2}\\ =23\end{array}$

Therefore, the coordinate of the midpoint is 23.

b. Step 1- Apply the concept of the average of numbers.

The average of two numbers is calculated by adding up all the numbers, then dividing the total by the count of numbers.

Step 2- Find the sum of the numbers.

Here the numbers are $-3$and 7.

Calculate the sum of the numbers as follows:

$\begin{array}{c}\text{Sumofthenumbers}=-3+7\\ =4\end{array}$

Count of the numbers =2

Step 3- Find the average.

Divide the sum of the numbers to the count of the numbers to find the average of the numbers as follows:

$\begin{array}{c}\text{Average}=\frac{4}{2}\\ =2\end{array}$

Therefore, the coordinate of the midpoint is 2.

c. Step 1- Apply the concept of the average of numbers.

The average of two numbers is calculated by adding up all the numbers, then dividing the total by the count of numbers.

Step 2- Find the sum of the numbers.

Here the numbers are 17 and $-9$.

Calculate the sum of the numbers as follows:

$\begin{array}{c}\text{Sumofthenumbers}=17-9\\ =8\end{array}$$\begin{array}{c}\text{Sumofthenumbers}=17-9\\ =8\end{array}$

Count of the numbers =2

Step 3- Find the average.

Divide the sum of the numbers to the count of the numbers to find the average of the numbers as follows:

$\begin{array}{c}\text{Average}=\frac{8}{2}\\ =4\end{array}$

Therefore, the coordinate of the midpoint is 23.

d. Step 1- Apply the concept of the average of numbers.

The average of two numbers is calculated by adding up all the numbers, then dividing the total by the count of numbers.

Step 2- Find the sum of the numbers.

Here the numbers areand$-7$.

Calculate the sum of the numbers as follows:

Count of the numbers =2$-5$