Question

calculate the distance between the points f = (-8, 8) and c = (-2, 1) 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 $(x_1,y_1)=(-8,8)$ and $(x_2,y_2)=(-2,1)$. Then $x_2 - x_1=-2-(-8)=6$ and $y_2 - y_1=1 - 8=-7$.

Step3: Calculate squared - differences sum

$(x_2 - x_1)^2+(y_2 - y_1)^2=6^2+(-7)^2=36 + 49=85$.

Step4: Find distance

$d=\sqrt{85}$.

Answer:

$\sqrt{85}$