Question

calculate the distance between the points n = (-2, 0) and c = (6, 4) 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, $(x_1,y_1)=(-2,0)$ and $(x_2,y_2)=(6,4)$.

Step2: Substitute values

Substitute $x_1=-2,y_1 = 0,x_2=6,y_2 = 4$ into the formula: $d=\sqrt{(6-(-2))^2+(4 - 0)^2}=\sqrt{(6 + 2)^2+4^2}=\sqrt{8^2+4^2}$.

Step3: Calculate squares and sum

Calculate $8^2=64$ and $4^2 = 16$, then $8^2+4^2=64 + 16=80$. So $d=\sqrt{80}$.

Step4: Simplify square - root

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

Answer:

$4\sqrt{5}$