Question

what is the distance between the points shown on the coordinate plane below? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify the coordinates

Let the first point be $(-5, - 4)$ and the second point be $(0,-6)$.

Step2: Apply 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, $x_1=-5,y_1 = - 4,x_2=0,y_2=-6$. So $d=\sqrt{(0-(-5))^2+((-6)-(-4))^2}=\sqrt{(0 + 5)^2+(-6 + 4)^2}$.

Step3: Simplify the expression inside the square - root

$(0 + 5)^2=25$ and $(-6 + 4)^2=(-2)^2 = 4$. Then $d=\sqrt{25 + 4}=\sqrt{29}$.

Step4: Calculate the approximate value

$\sqrt{29}\approx5.4$.

Answer:

$5.4$