Question

find the distance between the points (-11, -17) and (19, 2). round decimals to the nearest tenth. units

Explanation:

Step1: Identify 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, $x_1=-11,y_1 = - 17,x_2=19,y_2 = 2$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=19-(-11)=19 + 11=30$, $y_2 - y_1=2-(-17)=2 + 17 = 19$.

Step3: Square the differences

Square the results from Step 2. $(x_2 - x_1)^2=30^2 = 900$, $(y_2 - y_1)^2=19^2=361$.

Step4: Sum the squared - differences

Add the two squared values: $(x_2 - x_1)^2+(y_2 - y_1)^2=900 + 361=1261$.

Step5: Calculate the square - root

$d=\sqrt{1261}\approx35.5$.

Answer:

$35.5$