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 $(-6, - 4)$ and the second point be $(0,1)$.

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, $x_1=-6,y_1 = - 4,x_2=0,y_2 = 1$. So $d=\sqrt{(0-(-6))^2+(1 - (-4))^2}=\sqrt{(6)^2+(5)^2}$.

Step3: Calculate the squares

$(6)^2=36$ and $(5)^2 = 25$. Then $d=\sqrt{36 + 25}=\sqrt{61}$.

Step4: Approximate the value

$\sqrt{61}\approx7.8$.

Answer:

$7.8$