Question

find the distance between the points (2, -15.2) and (-11, 4.1). 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, $x_1 = 2$, $y_1=-15.2$, $x_2=-11$, $y_2 = 4.1$.

Step2: Calculate $(x_2 - x_1)$ and $(y_2 - y_1)$

$x_2 - x_1=-11 - 2=-13$; $y_2 - y_1=4.1-(-15.2)=4.1 + 15.2 = 19.3$.

Step3: Calculate $(x_2 - x_1)^2$ and $(y_2 - y_1)^2$

$(x_2 - x_1)^2=(-13)^2 = 169$; $(y_2 - y_1)^2=(19.3)^2=372.49$.

Step4: Calculate $(x_2 - x_1)^2+(y_2 - y_1)^2$

$(x_2 - x_1)^2+(y_2 - y_1)^2=169 + 372.49=541.49$.

Step5: Calculate the distance $d$

$d=\sqrt{541.49}\approx23.3$.

Answer:

$23.3$