Question

calculate the distance between the points e=(1, -2) and n=(9, -9) 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 $(x_1,y_1)=(1,-2)$ and $(x_2,y_2)=(9,-9)$. Then $x_2 - x_1=9 - 1 = 8$ and $y_2 - y_1=-9-(-2)=-9 + 2=-7$.

Step3: Calculate distance

$d=\sqrt{(8)^2+(-7)^2}=\sqrt{64 + 49}=\sqrt{113}$.

Answer:

$\sqrt{113}$