Question

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

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=-4-(-9)=-4 + 9 = 5$.
$y_2 - y_1=-4 - 9=-13$.

Step3: Square the differences

$(x_2 - x_1)^2=5^2 = 25$.
$(y_2 - y_1)^2=(-13)^2=169$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 169=194$.

Step5: Calculate the distance

$d=\sqrt{194}\approx13.9$.

Answer:

$13.9$