Question

find the distance between the points (16, 4) and (-9, -18). 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, $x_1 = 16$, $y_1 = 4$, $x_2=-9$, $y_2=-18$.

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

$x_2 - x_1=-9 - 16=-25$ and $y_2 - y_1=-18 - 4=-22$.

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

$(x_2 - x_1)^2=(-25)^2 = 625$ and $(y_2 - y_1)^2=(-22)^2 = 484$.

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

$(x_2 - x_1)^2+(y_2 - y_1)^2=625 + 484=1109$.

Step5: Calculate the distance $d$

$d=\sqrt{1109}\approx33.3$.

Answer:

$33.3$