Question

calculate the distance between the points g = (-8, 9) and c = (-1, 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-8,9)$ and $(x_2,y_2)=(-1,1)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-1-(-8)=-1 + 8=7$, $y_2 - y_1=1 - 9=-8$.

Step3: Square the differences

$(x_2 - x_1)^2=7^2 = 49$, $(y_2 - y_1)^2=(-8)^2=64$.

Step4: Sum and square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{49 + 64}=\sqrt{113}$.

Answer:

$\sqrt{113}$