Question

find the distance between the points (8, -8) and (3, 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, $(x_1,y_1)=(3,4)$ and $(x_2,y_2)=(8, - 8)$.

Step2: Calculate differences

$x_2 - x_1=8 - 3=5$ and $y_2 - y_1=-8 - 4=-12$.

Step3: Square the differences

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=(-12)^2 = 144$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 144=169$.

Step5: Calculate the square - root

$d=\sqrt{169}=13$.

Answer:

$13$