Question

find the distance between the points (8, 1) and (1, 6). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(8,1)$ and $(x_2,y_2)=(1,6)$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=1 - 8=-7$ and $y_2 - y_1=6 - 1 = 5$.

Step3: Square the differences

$(x_2 - x_1)^2=(-7)^2 = 49$ and $(y_2 - y_1)^2=5^2 = 25$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 25=74$.

Step5: Calculate the distance

$d=\sqrt{74}\approx8.6$.

Answer:

$8.6$