Question

find the distance between the points (-16.2, -18.2) and (3, -4.4). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign values

Let $(x_1,y_1)=(-16.2,-18.2)$ and $(x_2,y_2)=(3,-4.4)$. Then $x_2 - x_1=3-(-16.2)=19.2$ and $y_2 - y_1=-4.4 - (-18.2)=13.8$.

Step3: Calculate squares

$(x_2 - x_1)^2=(19.2)^2 = 368.64$ and $(y_2 - y_1)^2=(13.8)^2=190.44$.

Step4: Sum of squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=368.64 + 190.44=559.08$.

Step5: Calculate distance

$d=\sqrt{559.08}\approx23.6$.

Answer:

$23.6$