Question

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

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign values

Let $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(6, - 6)$. Then $x_2 - x_1=6 - 0 = 6$ and $y_2 - y_1=-6 - 2=-8$.

Step3: Calculate squared differences

$(x_2 - x_1)^2=6^2 = 36$ and $(y_2 - y_1)^2=(-8)^2 = 64$.

Step4: Sum squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 64=100$.

Step5: Take square - root

$d=\sqrt{100}=10$.

Answer:

$10$