Question

Find the distance and midpoint for each set of ordered pairs rounded to the nearest hundredth as needed.

Answer 1

The distance between the points is:

`2.83\text{ units}`

The midpoint is at;

`(3,8)`

Step-by-step explanation:

Given the set of ordered pairs;

`(2,7),(4,9)`

Firstly, let us find the distance between the two points.

The formula for calculating the distance between two points is;

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

substituting the given coordinates;

`\begin{gathered} (x_1,y_1)=(2,7) \\ (x_2,y_2)=(4,9) \\ d=\sqrt[]{(4-2)^2+(9-7)^2} \\ d=\sqrt[]{2^2+2^2} \\ d=\sqrt[]{8} \\ d=2.83 \end{gathered}`

Secondly, let us find the midpoint;

`\begin{gathered} x=(x_1+x_2)/(2) \\ y=(y_1+y_2)/(2) \end{gathered}`

substituting the coordinates;

`\begin{gathered} x=(2+4)/(2)=(6)/(2) \\ x=3 \\ y=(7+9)/(2)=(16)/(2) \\ y=8 \\ \text{midpoint = (3,8)} \end{gathered}`