Question

find the distance between the points (-8, -10) and (4, 4). 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, $(x_1,y_1)=(-8,-10)$ and $(x_2,y_2)=(4,4)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=4-(-8)=4 + 8=12$, and $y_2 - y_1=4-(-10)=4 + 10 = 14$.

Step3: Square the differences

Square the results from step 2. $(x_2 - x_1)^2=12^2 = 144$ and $(y_2 - y_1)^2=14^2=196$.

Step4: Sum the squared differences

Add the two squared - values: $(x_2 - x_1)^2+(y_2 - y_1)^2=144 + 196=340$.

Step5: Calculate the square - root

$d=\sqrt{340}\approx18.4$.

Answer:

$18.4$