Question

find the distance between the pair of points. (5,8) and (17,17)
the distance between the points is units. (round to two decimal places as needed.)

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 5,y_1 = 8,x_2=17,y_2 = 17$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=17 - 5=12$ and $y_2 - y_1=17 - 8 = 9$.

Step3: Square the differences

Square the results from Step 2. $(x_2 - x_1)^2=12^2 = 144$ and $(y_2 - y_1)^2=9^2 = 81$.

Step4: Sum the squared - differences

Add the two squared results: $144+81 = 225$.

Step5: Calculate the square - root

Take the square - root of the sum: $d=\sqrt{225}=15.00$.

Answer:

$15.00$