Question

find the distance between the pair of points (21, - 12) and (10, - 19). (round to the nearest thousandth as needed.) the distance is □.

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, $(x_1,y_1)=(21,- 12)$ and $(x_2,y_2)=(10,-19)$.

Step2: Calculate differences

$x_2 - x_1=10 - 21=-11$ and $y_2 - y_1=-19-(-12)=-19 + 12=-7$.

Step3: Square the differences

$(x_2 - x_1)^2=(-11)^2 = 121$ and $(y_2 - y_1)^2=(-7)^2 = 49$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=121 + 49=170$.

Step5: Calculate the square - root

$d=\sqrt{170}\approx13.0384$.

Answer:

$13.0384$