Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-8, -2) and (1, -4)

Explanation:

Step1: Recall 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, $x_1=-8,y_1 = - 2,x_2=1,y_2=-4$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=1-(-8)=9$ and $y_2 - y_1=-4 - (-2)=-2$.

Step3: Square the differences

Square the results from step 2. $(x_2 - x_1)^2=9^2 = 81$ and $(y_2 - y_1)^2=(-2)^2 = 4$.

Step4: Sum and square - root

Sum the squared differences and take the square - root. $d=\sqrt{81 + 4}=\sqrt{85}\approx9.2$.

Answer:

$9.2$