Question

find the distance between the points (-20, -6) and (-10, 16). 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, $x_1=-20,y_1 = - 6,x_2=-10,y_2 = 16$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-10-(-20)=-10 + 20=10$, $y_2 - y_1=16-(-6)=16 + 6=22$.

Step3: Square the differences

$(x_2 - x_1)^2=10^2 = 100$, $(y_2 - y_1)^2=22^2=484$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=100 + 484=584$.

Step5: Calculate the square - root

$d=\sqrt{584}\approx24.2$.

Answer:

$24.2$