Question

calculate the distance between the points j=(0, 6) and p=(-3, -2) in the coordinate plane. give an exact answer (not a decimal approximation). distance:

Explanation:

Step1: Recall 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, $(x_1,y_1)=(0,6)$ and $(x_2,y_2)=(-3,-2)$.

Step2: Substitute values

Substitute the values into the formula: $d=\sqrt{(-3 - 0)^2+(-2 - 6)^2}=\sqrt{(-3)^2+(-8)^2}$.

Step3: Calculate squares

Calculate the squares: $(-3)^2 = 9$ and $(-8)^2=64$. So $d=\sqrt{9 + 64}$.

Step4: Simplify

$d=\sqrt{73}$.

Answer:

$\sqrt{73}$