Question

calculate the distance between the points c=(0, - 2) and g=(8, 4) 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 $(x_2,y_2)=(8,4)$. Then $x_2 - x_1=8 - 0 = 8$ and $y_2 - y_1=4-( - 2)=4 + 2=6$.

Step3: Calculate squares

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

Step4: Sum squares

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

Step5: Calculate distance

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

Answer:

$10$