Question

find the distance between the points (3, 10) and (-9, -6). round decimals to the nearest tenth.

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, $(x_1,y_1)=(3,10)$ and $(x_2,y_2)=(-9,-6)$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=-9 - 3=-12$.
$y_2 - y_1=-6 - 10=-16$.

Step3: Square the differences

$(x_2 - x_1)^2=(-12)^2 = 144$ and $(y_2 - y_1)^2=(-16)^2 = 256$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=144 + 256=400$.

Step5: Calculate the square - root

$d=\sqrt{400}=20$.

Answer:

$20$