Question

find the distance between the points (10, 8) and (-8, 2). 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, $(x_1,y_1)=(-8,2)$ and $(x_2,y_2)=(10,8)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=10-(-8)=18$, $y_2 - y_1=8 - 2 = 6$.

Step3: Square the differences

$(x_2 - x_1)^2=18^2 = 324$ and $(y_2 - y_1)^2=6^2 = 36$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=324 + 36=360$.

Step5: Calculate the square - root

$d=\sqrt{360}\approx18.973666$.

Step6: Round to the nearest tenth

Rounding $18.973666$ to the nearest tenth gives $19.0$.

Answer:

$19.0$