Question

find the distance between the pair of points. (1, - 16) and (-16, - 22). the distance is (round to the nearest thousandth as needed.)

Explanation:

Step1: Recall 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, $(x_1,y_1)=(1, - 16)$ and $(x_2,y_2)=(-16,-22)$.

Step2: Calculate differences

$x_2 - x_1=-16 - 1=-17$ and $y_2 - y_1=-22-( - 16)=-22 + 16=-6$.

Step3: Square the differences

$(x_2 - x_1)^2=(-17)^2 = 289$ and $(y_2 - y_1)^2=(-6)^2 = 36$.

Step4: Sum squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=289 + 36=325$.

Step5: Calculate square - root

$d=\sqrt{325}\approx18.027756$.

Step6: Round to nearest thousandth

$d\approx18.028$.

Answer:

$18.028$