Question

find the distance between the points (2, 10) and (8, 4). round decimals to the nearest tenth.

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, $x_1 = 2,y_1 = 10,x_2 = 8,y_2 = 4$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=8 - 2=6$ and $y_2 - y_1=4 - 10=-6$.

Step3: Square the differences and sum

$(x_2 - x_1)^2+(y_2 - y_1)^2=6^2+( - 6)^2=36 + 36=72$.

Step4: Calculate the square - root

$d=\sqrt{72}\approx8.5$.

Answer:

$8.5$