Question

find the distance between the points (-2, 1) and (-8, -7). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let $(x_1,y_1)=(-2,1)$ and $(x_2,y_2)=(-8,-7)$.

Step2: Calculate the differences in x - and y - coordinates

$x_2 - x_1=-8-(-2)=-8 + 2=-6$ and $y_2 - y_1=-7 - 1=-8$.

Step3: Square the differences

$(x_2 - x_1)^2=(-6)^2 = 36$ and $(y_2 - y_1)^2=(-8)^2=64$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 64=100$.

Step5: Take the square - root

$d=\sqrt{100}=10$.

Answer:

10