Question

find the distance between the points (19, -5) and (3, -16). round decimals to the nearest tenth. units

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, $x_1 = 19,y_1=-5,x_2 = 3,y_2=-16$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=3 - 19=-16$, $y_2 - y_1=-16-(-5)=-16 + 5=-11$.

Step3: Square the differences

Square the results from step 2. $(-16)^2 = 256$ and $(-11)^2 = 121$.

Step4: Sum the squared - differences

Add the squared differences: $256+121 = 377$.

Step5: Calculate the square - root

$d=\sqrt{377}\approx19.4$.

Answer:

$19.4$