Question

find the distance between the points (-8, -2) and (1, 10). round decimals to the nearest tenth. units

Explanation:

Step1: Identify the distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign the values of the points

Let $(x_1,y_1)=(-8,-2)$ and $(x_2,y_2)=(1,10)$. Then $x_2 - x_1=1-(-8)=9$ and $y_2 - y_1=10 - (-2)=12$.

Step3: Calculate the squares

$(x_2 - x_1)^2=9^2 = 81$ and $(y_2 - y_1)^2=12^2 = 144$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 144=225$.

Step5: Calculate the square - root

$d=\sqrt{225}=15$.

Answer:

15