Question

1. find the distance between the two points rounding to the nearest tenth (if necessary). (0, - 5) and (-3, -9)

Explanation:

Step1: Identify the 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, $(x_1,y_1)=(0, - 5)$ and $(x_2,y_2)=(-3,-9)$.

Step2: Substitute the values

Substitute $x_1 = 0,y_1=-5,x_2=-3,y_2 = - 9$ into the formula:
$d=\sqrt{(-3 - 0)^2+(-9+5)^2}=\sqrt{(-3)^2+(-4)^2}$.

Step3: Calculate the squares

$(-3)^2=9$ and $(-4)^2 = 16$, so $d=\sqrt{9 + 16}$.

Step4: Calculate the sum inside the square - root

$9+16 = 25$, so $d=\sqrt{25}$.

Step5: Find the square - root

$\sqrt{25}=5$.

Answer:

$5$