Question

calculate the distance between the points k=(2, 0) and m=(-2, 8) in the coordinate plane. give an exact answer (not a decimal approximation).

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

Step2: Substitute values

Substitute the values into the formula: $d=\sqrt{(-2 - 2)^2+(8 - 0)^2}=\sqrt{(-4)^2+8^2}$.

Step3: Calculate squares

Calculate the squares: $(-4)^2 = 16$ and $8^2=64$. So $d=\sqrt{16 + 64}$.

Step4: Simplify sum

Simplify the sum inside the square - root: $16+64 = 80$. So $d=\sqrt{80}$.

Step5: Simplify square - root

Simplify $\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}$.

Answer:

$4\sqrt{5}$